In a food processor or with a mixer, combine the butter and honey until well blended. Refrigerate the honey butter if you don’t plan to use it within a couple of hours. Return the mixture to room temperature before using.

In a large mixing bowl, stir together the flour, salt, baking powder, and, if you wish, the sugar. Pour in the oil and mix with your fingertips to combine. Add the water and the milk, working the liquids into the flour until a sticky dough forms.

Lightly dust a counter or pastry board with flour and knead the dough vigorously for 1 minute. The mixture should be “earlobe” soft and no longer sticky. Let the dough rest, covered with a damp cloth, for 15 minutes. Divide the dough into 3 balls, cover the balls with the damp cloth, and let them rest for another 15 to 30 minutes. (The dough can be refrigerated at this point for up to 4 hours.)

Lightly dust a counter or pastry board with flour again and roll out each ball of dough into a circle or oval approximately 1/8 to ¼ inch thick. If you have a tortilla roller, use it rather than a heavier rolling pin, which compacts the dough more. Trim off any ragged edges and discard them. To avoid toughening the dough, try not to reroll it. Cut each circle of dough into 4 wedges.

In a heavy, high-sided saucepan or skillet, heat the oil to 400. F. Carefully transfer 2 to 3 wedges of dough to the oil. After sinking briefly, the sopaipillas should begin to balloon and rise back to the surface. Spoon some oil over the tops of the sopaipillas. When the top surfaces are fully puffed, a matter of seconds, turn the sopaipillas. Cook just until the sopaipillas are light golden, and drain.

Arrange the sopaipillas in a napkin-lined basket and serve immediately with honey butter. Puncture the sopaipillas as you eat them, filling the center with a drizzle of the butter.

Regional Variations: New Mexicans sometimes eat unsweetened stuffed sopaipillas as a main dish. They can be filled with almost any combination of meat and beans, but they are particularly delicious bulging with New Mexico Carne Adovada and topped with chopped tomato and lettuce.