Inspired by Nebraska's Runzas and Michigan's pasties, these pocket pies hold beef, sausage, onion, and shredded greens. The crust is like a buttery, flaky Cheez-It, but pastry-phobes can use purchased pie crust and add cheddar to the filling.
For pastry: In a food processor, combine flour, cheese, sugar, salt and baking powder. Pulse a few times to blend. Sprinkle half of the cold butter pieces over the dry ingredients. Process until the mixture resembles cornmeal, about 15 seconds. Add the remaining cold butter and pulse until remaining butter cubes are broken down by about half, about 10 times.
In a measuring cup, combine ice water and vinegar. Add about three-fourths of the vinegar-water to food processor. Pulse until dough begins to form a few small clumps, about 10 times. Test dough by squeezing a small amount in the palm of your hand. If it easily holds together and your palm isn't dusty with floury bits, it's ready. If not, add an additional 1 1/2 teaspoons vinegar-water and pulse 2 or 3 more times. Repeat this process as needed until dough just holds together. Turn out onto a work surface. Briefly gather and knead dough until uniform. Divide dough into 12 equal portions. Shape each into a disk and wrap tightly in plastic wrap. Chill dough at least 2 hours or until easy to handle.
For hand pies: In a large skillet, heat oil over medium-high heat. Add beef, sausage, onion and garlic. Cook until browned, about 5 minutes. Drain off fat. Add shredded vegetables and Worcestershire sauce; cook until wilted and tender, about 8 minutes. Season with salt and pepper. Remove from heat; let filling cool completely.
Preheat oven to 400°. For egg wash, in a small cup, whisk together egg, the 1 tablespoon water and a pinch of salt. Set aside. For each pie, on a lightly floured surface, roll a piece of dough into a 6-inch circle. Place 1/3 cup filling on bottom half of circle. Brush edge of circle with egg wash. Fold unfilled side of circle over filling; crimp edges with a fork to seal. Evenly space hand pies on an extra-large baking sheet. Cut a few slits in tops of hand pies to vent. Lightly brush tops of hand pies with egg wash.
Bake 15 minutes. Reduce oven temperature to 350°. Bake until golden on the tops and browned and crisp on the bottoms, about 25 minutes. Let cool slightly before serving.