Heat the garlic and oil in a large skillet over medium heat. Cook, stirring, until the garlic becomes golden brown, about 2 minutes. Add the scallions and cook, stirring, just until bright green and tender, about 1 minute. Transfer half the garlic-scallion mixture to a medium serving bowl, stir in the sour cream, and refrigerate until ready to serve.
Add the beef and pepper to the skillet and sprinkle lightly with salt and pepper. Raise the heat to high and cook, stirring to break the beef into small bits, until the meat is browned and cooked through, about 4 minutes. Stir in the chili powder, then the tomato paste. Cook, stirring, for 30 seconds. Remove from the heat, transfer to a rimmed baking sheet, and place in the freezer to cool quickly. When it's room temperature, stir in the cheese.
While the meat mixture cools, fill a Dutch oven with oil to a depth of 1 inch (about 7 cups). Heat to 375°F over medium heat.
Scoop 2 tablespoons meat filling in the center of a pastry round fold the pastry in half to enclose the filling. Seal the edges by decoratively crimping or pressing with the tines of a fork. Repeat to fill and seal 3 more, then add to the hot oil. Cook, turning to evenly brown, until golden brown and crisp, 2 to 3 minutes. Transfer with a slotted spatula to paper towels to drain. While the first batch fries, fill and seal 4 more empanadas. Cook after the first batch comes out. Repeat until all the empanadas are filled, sealed, and fried. Garnish the sour cream sauce with scallions and serve with the hot empanadas.