In bowl, whisk together flour, baking powder, salt and cayenne. Using pastry blender or two knives, cut in butter until mixture resembles coarse crumbs; stir in cheddar. Pour milk over top and stir with fork to form soft, ragged dough.
Turn onto a lightly floured surface and knead gently, just to form dough (it will look slightly dry but will bake up beautifully). Gently pat into a 9 x12-inch (22.5 cm x 30 cm) rectangle, about 1/2-inch (1 cm) thick. Cut into 12 3-inch (7.5 cm) squares and place about an inch apart on a parchment-lined baking sheet.
Brush top of biscuits with egg and bake in the centre of a 425 F (220 C) oven until golden, about 12 to 15 minutes. Let cool in pan on rack.
In large deep skillet, brown turkey over medium high heat until no longer pink, about 8 minutes. Stir in onion, celery and carrot. Let cook 5 minutes. Stir in garlic, chili powder and tomato paste and cook one minute more. Stir in chili sauce and diced tomatoes. Adjust heat to maintain a gentle simmer and cook just until sauce has thickened slightly, about 15 minutes.
To serve, split biscuits in half and top with turkey mixture.
Makes 4 to 6 servings