In a large nonstick skillet, warm oil over medium heat. Add carrot and onion; cook, stirring, until tender, 8 to 10 minutes. Stir in garlic; sauté for 1 minute. Increase heat to medium high. Add turkey and cook, stirring and breaking up meat, until browned, about 5 minutes. Add tomato paste, brown sugar, Worcestershire and chili powder. Cook, stirring, for 1 minute. Stir in broth, reduce heat and simmer until thickened but still saucy, about 4 minutes. Season with salt. Transfer mixture to a plate; let cool to room temperature.
Preheat oven to 425°F; line a large baking sheet with parchment. Cut both sheets of dough into quarters so you have 8 wedges. Divide filling evenly among pastry wedges, spooning filling on half of each wedge, from the curved edge toward the tip. Moisten edges with water and fold in half; pinch edges to seal. Crimp edges with tines of a fork, if desired. Place on baking sheet and bake until dough is golden brown and filling is hot, about 20 minutes. Serve hot, or let cool, cover and refrigerate until ready to pack for lunch.