Make the Blondie
Preheat the oven to 350°F (180°C) and butter and line a 9-inch (23cm) round cake pan. Set aside.
In a medium bowl, whisk the butter and sugar together until combined, then add the eggs and vanilla extract.
In a separate small bowl, mix the flour, salt and baking soda together, then stir this into the butter mixture until combined.
Spread the batter into your prepared pan and bake for about 30 minutes, until just set. Let cool completely in the pan. This can be made the day before.
Make the Caramel Ice Cream
In a medium bowl, whisk the egg yolks and salt together. Set aside.
Spread the sugar evenly over the bottom of a heavy, medium-sized saucepan and place over medium-low heat.
After 2 or 3 minutes, the sugar will begin to melt. With a wooden spoon, gently move the sugar in the saucepan to allow it to melt evenly without burning.
Once all of the sugar has melted and turned a deep amber color add the milk and stand back as it bubbles. When the bubbles have calmed down, whisk until the sugar is dissolved in the milk.
Add the caramel mixture to the egg yolks, one ladleful at a time while whisking constantly. Return the mixture to the saucepan and cook over medium-low heat, stirring constantly for about 3 minutes, until the mixture thickens to a custard-like consistency.
Turn off the heat and whisk in the vanilla.
Immediately strain the mixture through a sieve to give you a smooth custard. Set aside to cool down fully before moving on to the next step (you can put the custard in the fridge or you can place the bowl over a bowl of ice water to cool quickly). This custard base can be made up to 24 hours in advance if needed.
Once the custard is cold, whip the heavy cream in the bowl of a stand mixer fitted with a whisk attachment (or with a handheld electric mixer) on medium-high speed until thickened, about 3 minutes. Gently stir the whipped cream into the chilled custard until evenly mixed. Place in the fridge until needed.
Make the Banana Ice Cream
In a medium saucepan over medium-heat, cook the milk and banana gently for about 4 minutes.
Meanwhile, in another medium bowl, whisk the egg yolks, sugar and salt until smooth.
Once the milk is simmering, pour it, one ladleful at a time, into the egg mixture while whisking constantly.
Return the mixture to the pot and lower the heat to low. Cook, stirring constantly for 2 to 3 minutes, until a thick custard is formed.
Remove from the heat and stir in the vanilla.
Immediately strain the mixture through a sieve passing through as much banana as you can. Set aside to cool down fully before moving on to the next step (you can put the custard in the fridge or you can place the bowl over a bowl of ice water to cool quickly). This custard base can be made up to 24 hours in advance if needed.
Once the custard is cold, whip the heavy cream in the bowl of a stand mixer fitted with a whisk attachment (or with a handheld electric mixer) on medium-high speed until thickened, about 3 minutes. Gently stir the whipped cream into the chilled custard until evenly mixed. Place in the fridge until needed.
Assemble the Baked Alaska
Remove the blondie from the pan and using a 2-quart (or 1.8 liter) capacity bowl, check that it fits just inside the rim of the bowl. Trim away any excess blondie if need be and set aside.
Butter and line the bowl with 4 layers of plastic wrap, allowing some excess to hang about 5 inches (12 ½ cm) off the edges all around. Set aside.
Alternate adding scoops of caramel ice cream, banana ice cream and the caramel sauce into the prepared bowl. Fill it until you have about a ½ inch (2cm) of space at the top (you may not use all of the ice cream).
Using a large offset spatula, give the ice creams one quick swirl to create a ripple effect. Top with the blondie, cover well with the overhanging plastic wrap and freeze for at least six hours, but preferably overnight. (Any extra ice cream base can be frozen in a separate container.)
When Ready to Serve, Prepare the Meringue:
Place the egg whites, sugar, and cream of tartar in the top of a double boiler over simmering water and whisk constantly for 2 minutes until the sugar has dissolved.
Remove from the heat and beat the egg white mixture in a stand mixer fitted with a whisk attachment or with a handheld electric mixer on high speed until thick and glossy, and it holds stiff, glossy peaks when the beaters are lifted, 4 to 5 minutes.
Remove the ice cream from the freezer, unmold and place (blondie side down) on a serving plate. (If the ice cream is difficult to remove, run the bowl under warm tap water for a minute.)
Cover the ice cream and blondie with the meringue. Using a kitchen torch, toast the meringue until golden brown all over. This is best enjoyed immediately, but any leftovers can be put back in the freezer and served within two days.