Preheat the oven to 375°F (190°C).
Wash and cut up the peaches either into slices or chunks. I leave on the skin as it breaks down during baking but that is up to you.
Toss the peaches with ¼ cup sugar and let sit for 20 minutes in the bowl.
Strain off the liquid from the peaches and add to it (around 1/4 cup) the cornstarch, lemon juice, 1/4 teaspoon salt and vanilla paste. Add back in the peaches to the liquid and stir to coat.
Place the peach filling in a small 8" x 8" baking dish.
Bake the peaches for 10 minutes to cook and reduce.
While peaches bake, make the biscuit topping: In a bowl, whisk together flour, baking powder, baking soda, 1 tablespoon of sugar, and remaining 1/4 teaspoon of salt.
Rub butter into the flour mixture using your fingers until it resembles coarse bread crumbs.
Stir in yogurt (or sour cream) until just combined and dough holds together. Be careful not to overmix as it will toughen.
Remove peaches from the oven and scatter the biscuit topping in mounds on top. Return to the oven.
Bake for 40-45 minutes, until juices are bubbling and biscuits are golden brown.
Let cool for 20 minutes. Serve warm with whipped cream or vanilla ice cream. Store leftovers in the fridge for up to 3 days.