Combine flour, salt, baking powder, and sugar in a bowl.
Cut in shortening until mixture looks like coarse meal.
Stir in the milk with a fork until it comes together in a moist dough.
Form into a ball and knead several times. Let the dough rest for 30 minutes.
Roll out the dough on a lightly floured surface into an 1/8” thickness.
Cut into (handheld size) squares or triangles. (I used a pizza cutter for cutting the dough.)
Heat oil to 375ºF in a deep pan.
Fry the dough (2 or 3 at a time, at the most) turning often until golden on all sides.
This should take place very quickly, about 30 seconds.
Remove the cooked sopaipillas from the oil using a spatula and drain on paper towels. Repeat frying the rest.
Drizzle with honey and serve immediately.