Stuffed Jalapeno Sliders

Stuffed Jalapenos:
1 tablespoon olive oil
1/2 small onion, diced
1/4 pound extra-lean ground beef
2 tablespoons water
1 1/2 teaspoons taco seasoning
1/2 cup grated Chihuahua cheese
5 large jalapeno peppers
Tiny Burger Buns:
1/4 cup lukewarm water
2 tablespoons white sugar
2 teaspoons active dry yeast
1 1/2 cups all-purpose flour
2 small eggs, beaten, divided
2 tablespoons milk
1 tablespoon unsalted butter, melted
40 toothpicks

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 degrees F (175 degrees 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 degrees F (190 degrees C). Brush tops of buns with beaten egg.
Bake buns in the preheated oven until tops are golden brown, 6 to 7 minutes. Transfer to a cooling rack and let cool, about 10 minutes.
Reduce oven temperature to 200 degrees F (95 degrees C).
Slice cold jalapeno peppers into 1/4-inch thick rings. Cut buns in half. Sandwich jalapeno pepper rings in the buns and secure with a toothpick. Arrange sliders in a casserole dish. Cover with aluminum foil.
Bake sliders in the preheated oven until warmed through, about 10 minutes.