In a large pan, heat olive oil over medium heat. Add onion and cook until soft, about 5 minutes. Add garlic and carrots and cook until fragrant, about 1 minute more.
Add crumbled ground beef to the onion mixture and cook, stirring, until the fat and juices begin to release, 3 - 4 minutes. Add spices and sauté for a few minutes until fragrant. dd the tomato paste and tomato sauce and adjust the consistency with water. Cook until the beef is cooked through and the carrots are soft, 10 - 12 minutes. Add the peas, corn and vinegar, stir briefly and remove from heat. Set aside to cool.
To form hand pies, roll prepared Bob's Red Mill Gluten Free Pie Crust between two large pieces of parchment paper or plastic wrap to 1/8-inch thickness. Cut eight 15x20 cm rectangles, rerolling the dough as necessary. Line a baking sheet with parchment paper.
Place 1/2 cup of the beef and vegetable filling (120g) on the lower third of each rectangle, leaving a border of about 1/4-inch. Brush the border edge with water to help seal. Gently fold the empty top third of the rectangle over the filling, using the parchment paper or plastic wrap to aide in maneuvering the dough. Press the edges to seal and use the tines of a fork to crimp shut. Gently transfer the formed hand pie to the prepared baking sheet. Repeat until all pies are formed then freeze for at least 1 hour.
To bake the hand pies, preheat the oven to 400°F. Thoroughly whisk together 1 egg and 1 Tbsp water. Brush each frozen hand pie with eggwash and cut two to three vents in the top using a sharp knife.
Bake hand pies until the crust is golden, 30 - 35 minutes.
Let cool about 5 minutes. These can be eaten warm or at room temperature.