Heat oil in a skillet over medium heat. Add onion; cook and stir until soft, about 5 minutes. Add beef; cook, stirring to break into very small pieces, until browned, about 5 minutes. Drain any excess grease. Stir in 2 tablespoons water and taco seasoning; cook until water evaporates, about 5 minutes.

Let beef mixture cool completely, about 10 minutes. Stir in Chihuahua cheese.

Preheat oven to 350°F (175°C).

Cut tops off jalapeno peppers and scoop out seeds and ribs. Stuff with beef mixture, using the thick end of a chopstick to pack in mixture. Stack upright against the edge of a casserole dish.

Bake in the preheated oven until jalapeno peppers are soft, about 45 minutes.

Refrigerate jalapeno peppers until stuffing firms up, 1 to 2 hours.

Combine 1/4 cup water, sugar, and yeast in a small bowl. Let stand until foamy, about 5 minutes.

Combine flour, 1 egg, milk, and butter in a large bowl. Pour in yeast mixture; mix until well combined. Turn dough onto a lightly floured surface and knead until mostly smooth but slightly sticky, about 5 minutes.

Form dough into a ball and place in a lightly greased bowl. Cover with a towel and let rise, about 20 minutes.

Line a baking sheet with parchment paper. Turn dough out onto a floured surface; push down to knock out air. Form into 1-inch buns and arrange 1 inch apart on the baking sheet. Cover with the towel and let rise until puffy, about 1 hour.

Preheat oven to 375°F (190°C). Brush tops of buns with beaten egg. Bake buns in the preheated oven until tops are golden brown, 6 to 7 minutes.

Reduce oven temperature to 200°F (95°C).