In a medium saucepan over medium heat, combine the milk and fat.
After giving the pan a good stir to ensure all of the lard has melted, turn off the heat and let it cool for five minutes.
Whisk the eggs and vanilla extract together until a custard forms, then let it cool in your stand mixer fitted with a dough hook attachment.
Combine the flour, baking soda, salt, cinnamon, and anise in a large bowl and whisk to combine thoroughly.
Once the stand mixer is operating at a medium speed, add the flour mixture and let the dough come together using the dough hook for 8 to 10 minutes, or until the dough forms a ball and stops clinging to the stand mixer's sides.
On a baking sheet that has been oiled, roll the dough into 20 balls.
After 40 minutes, cover and allow to rise.
Each ball should be formed into a 5-inch circle on a surface dusted with flour. To prevent them from drying out, cover them with a fresh kitchen towel and stack them with some flour sprinkled in between.
In a big skillet or saucepan, heat the oil to 350–365 degrees, approximately 1 inch deep.
Add the sugar, nutmeg, and cinnamon to a small basin and stir with a fork while the oil heats up.
After about 30 seconds on each side, fry each piece of buñuelos until golden brown, and then quickly coat both sides with the sugar mixture.
Continue with the remaining dough pieces.