In a bowl, mix together the all-purpose flour and salt.
Add the cold, diced butter to the flour mixture. Utilizing a pastry cutter or your fingertips, incorporate the butter into the flour until the mixture takes on the texture of coarse crumbs.
Stir in the sour cream and mix until the dough starts to come together.
Transfer the dough onto a lightly floured surface and gently knead it until it forms a smooth ball. Cover the dough with plastic wrap and place it in the refrigerator for a minimum of 30 minutes.
For the Filling
In a frying pan, warm a small amount of oil over medium heat. Add the finely chopped onion and garlic, and cook until they turn translucent.
Add the ground meat and cook until it's browned and cooked through. Break it into small crumbles as it cooks.
Stir in the mashed potatoes, grated carrots, dried thyme, paprika, salt, and pepper. Cook for a few more minutes until the mixture is well combined and heated through. Remove from heat and let it cool slightly.
Assembly
Before you begin, preheat your oven to 375°F (190°C) and prepare a baking sheet by lining it with parchment paper.
Take the chilled dough and roll it out on a floured surface into a large, thin rectangle, about 1/8 inch thick.
With a circular cookie cutter or a glass, create round shapes by cutting through the dough. Place a spoonful of the meat and vegetable filling in the center of each circle.
Fold the dough over the filling to form a half-moon shape. Press the edges with a fork to seal them tightly. You can also make a decorative edge by twisting the dough with your fingers.
Place the filled pies on the prepared baking sheet.
Baking
Brush the tops of the pies with a beaten egg or a bit of milk to give them a golden color when baked.
Bake in the preheated oven for about 20-25 minutes, or until the pies are golden brown and crispy.
Serving
Once baked, let the Filled Baltic Pies cool for a few minutes before serving. They are delicious when served warm.