In a small bowl combine the boiling water and anise seeds and let steep until the water cools but is still warm, about 15 minutes. Strain out and discard the seeds, reserving the tea.
In a medium bowl combine the flour, sugar, baking powder, and salt.
In a separate bowl, whisk together the egg, butter, and vanilla and combine. Add the warm anise tea and mix until a soft and smooth dough is formed. Cover and let the dough rest for 30 minutes.
While the dough is resting, mix together the sugar and cinnamon for the cinnamon sugar. Set aside.
After the dough has rested, divide it into 12 equal portions, each 4 oz/115g. Cover with cling wrap and allow to rest again for about 15 minutes.
On a floured surface, roll the dough as thinly as possible to about 7 ½-inches in diameter. You can stack the rolled portions between sheets of parchment to prevent sticking.
Heat about 2-inches of oil in a medium frying pan and set up a baking sheet lined with a wire rack or paper towels on the counter next to the pan. Place a bowl of cinnamon sugar nearby.
When the oil is hot (about 350°F/180°c), fry the buñuelos for a minute or two, pressing down into the oil, until golden brown. Flip and fry the other side for a minute or two, until golden brown.
Transfer to the rack and let drain for a minute, and then sprinkle with cinnamon sugar while still hot. Repeat with the remaining buñuelos.
Best enjoyed straight away! Store cooled buñuelos in an airtight container for up to 1 day.