For the pickled jalapeños:
2 cups distilled white vinegar
1 cup water
2 tablespoons kosher salt
2 teaspoons granulated sugar
4 medium jalapeño chiles, stemmed and cut into 1/8-inch-thick slices
For the pierogi filling:
1 cup (4 ounces) finely shredded Monterey Jack, Cheddar, or block mozzarella cheese
1/2 cup (4 ounces) cream cheese, at room temperature
2 tablespoons unbleached all-purpose flour
1/2 teaspoon kosher salt
1/2 teaspoon garlic powder
1/2 teaspoon onion powder
For the cornmeal dough and coating:
2 large eggs
1/2 cup (4 ounces) sour cream or plain Greek yogurt (full-fat, reduced-fat, or nonfat)
3 tablespoons (1 1/2 ounces) unsalted butter, melted and slightly cooled
1 teaspoon kosher salt
1 1/2 cups (6 3/8 ounces) unbleached all-purpose flour
1/2 cup (2 ounces) corn flour
2 tablespoons finely ground cornmeal + 1 cup finely ground cornmeal for breading
1 tablespoon water
Make the pickled jalapeños: Bring the vinegar, water, salt, and sugar to a simmer in a medium saucepan over medium heat and stir until the salt and sugar dissolve. Add the jalapeño slices and simmer until their color changes from bright green to dull olive, about 1 minute. Pour into a bowl and let stand for at least 1 hour at room temperature or up to 1 week in the refrigerator.
Make the filling: Blend the shredded cheese, cream cheese, flour, salt, garlic powder, and onion powder with a hand-held mixer or stand mixer fitted with the paddle attachment on medium-low speed until the filling is thick and homogenous. Refrigerate until firm, about 1 hour. (Or make the filling up to 1 week in advance and store, tightly covered, in the refrigerator.)
Make the dough: Whisk 1 egg, sour cream or yogurt, butter, and salt in a bowl. Whisk all-purpose flour, corn flour, and 2 tablespoons cornmeal in a large bowl. Gently stir wet ingredients into flour. The dough will initially be very dry and shaggy, seeming as if it will never come together, but have no fear: Keep stirring, and it will pull itself into shape.
Once the dough starts to come together, press and smash it against the sides of the bowl with your palms, picking up dough bits and essentially kneading it within the bowl until it forms a ball.
Tip dough and any remaining shaggy flakes out onto a clean work surface or Roul’Pat. Knead until smooth, about 1 minute. Cover dough with the bowl and let rest 15 minutes.
Whisk remaining egg and water in a small bowl for egg wash.