Whisk together the 1 1/2 cups flour, the sugar, salt, and yeast in a large bowl. Stir in the warmed milk followed by the 3 tablespoons canola oil, egg yolks, vanilla, and liquor.
Use an electric mixer to beat for 2 minutes on high speed. Stir in enough extra flour (up to 1/4 cup) until the dough holds together.
Turn the dough out onto a floured work surface and knead 50 turns. Cover with plastic wrap, then let rest 10 minutes.
While it’s resting, make the custard filling. In a saucepan, combine 1/4 cup sugar and 1 tablespoon cornstarch. Slowly stir in the milk and egg yolk. Bring to a boil, stirring constantly, and cook for about a minute until thick (it’ll thicken more as it cools). Cool thoroughly before using (refrigerating if you need to).
Line a large baking sheet with parchment paper. Once the dough is done resting, turn it back out onto a floured surface and roll the dough int a 1/2″ thick disk. Cut out circles using a 2 1/2″ round cutter dipped in flour. Re-roll the scraps and cut out the circles again.
Place the cut rounds on the baking sheet and cover with a towel, letting rise at room temperature for 1 hour.
Pour the canola oil into a large Dutch oven and heat the oil to 360F. Once the oil reaches temperature, use a heat resistant spatula or a shallow strainer to carefully drop the dough in, one at a time, cooking a maximum of 3 at once. Cook the doughnuts until they are a deep brown on one side, then turn the doughnut and cook the other side until it is roughly the same color. Remove the dough from the oil and place on a wire rack, letting any excess oil train off while they cool. Test the first dough round to make sure the inside is completely cooked, and adjust the cooking time accordingly if not. Repeat with the remaining dough rounds.
Fit a pastry bag with a long, slender tip and fill with the custard from the fridge. Pipe the filling into the dough rounds. Brush each side of the rounds with the melted butter then dip each side in the 1/3 cup of sugar for coating.
Serve immediately. Enjoy!
