Instructions

for the dough

Whisk flour, salt, and baking powder together in large bowl. Rub lard into flour mixture with your fingers until mixture resembles coarse meal. Stir in ¾ cup plus 2 tablespoons water until combined. Turn out dough onto clean counter and knead briefly to form cohesive ball, 6 to 8 turns. Divide dough into 8 equal portions, about 2¾ ounces each (scant ⅓ cup), then roll into balls. Transfer dough balls to plate, cover with plastic wrap, and refrigerate until firm, at least 30 minutes or up to 2 days.

for the refried beans

Heat lard in 12-inch skillet over medium heat until shimmering. Add onion and cook until softened, about 4 minutes. Stir in beans, broth, and salt. Cook, mashing beans with potato masher, until finely mashed and mixture is thickened, about 8 minutes. Season with salt to taste. Set aside and let cool completely.

for the green chile

Adjust oven rack 6 inches from broiler element and heat broiler. Line rimmed baking sheet with aluminum foil. Arrange Anaheims and jalapeño in single layer on prepared sheet. Broil until chiles are soft and mostly blackened, about 5 minutes per side, rotating sheet halfway through broiling. Transfer chiles to bowl and cover with plastic; let cool for 10 minutes.
Remove skins from chiles with spoon. Stem and seed Anaheims, then chop into ¼-inch pieces. Stem (but do not seed) jalapeño; chop into ¼-inch pieces.
Heat lard in large saucepan over medium heat until shimmering. Add onion and cook until, softened, about 3 minutes. Stir in garlic and cook until fragrant, about 30 seconds. Stir in flour and cook for 1 minute. Stir in broth, salt, Anaheims, and jalapeño and bring to simmer. Simmer until slightly thickened, about 6 minutes. Season with salt to taste; cover and set aside.
Keeping other dough balls covered with damp dish towel, roll 1 dough ball into 7-inch circle on lightly floured counter. Lightly squeeze ¼ cup cheese in your palm to form ball. Place cheese in center of dough round, followed by ¼ cup refried beans. Moisten edges of dough round with water. Fold dough round in half, creating half-moon shape to enclose filling, and press to seal.
Moisten top of sealed edge with water. Starting at 1 end, fold, slightly twist, and pinch dough diagonally across sealed edge between your thumb and index finger. Continue pinching and twisting dough around seam to create decorative rope edge. Transfer to parchment paper–lined baking sheet. Repeat with remaining dough balls, cheese, and refried beans (reserve any remaining beans for another use). Using paring knife, poke ½-inch hole in center of each turnover. (Filled turnovers can be covered and refrigerated for up to 24 hours.)
Line baking sheet with triple layer of paper towels. Add oil to large Dutch oven until it measures about 1½ inches deep and heat over medium-high heat to 375 degrees. Add 4 turnovers to oil and fry until golden brown, about 3 minutes per side. Adjust burner as needed to maintain oil temperature between 350 and 375 degrees. Transfer fried turnovers to prepared sheet. Return oil to 375 degrees and repeat with remaining 4 turnovers.
Reheat green chile sauce over medium-high heat until hot. Serve turnovers topped with chile sauce.