Combine dough ingredients and knead per directions. Cover and rest 60 minutes.

Preheat oven to 375°F. Roll dough into a 12x12 rectangle. Cut into 12 equal squares.

Place one sausage link, half a roasted Hatch chile, and half a slice of cheese on each square. Fold dough around filling and pinch firmly to seal. Place seam-side down on parchment-lined sheet pan. Let rise 1 hour.

Brush with egg wash. Bake 15 to 20 minutes until golden brown.