Preheat your oven to 425 degrees. In a bowl, whisk together flour, baking powder, baking soda, and ¼ teaspoon salt.
Cut butter into flour mixture with a pastry cutter (or two knives) until mixture is crumbly. Stir in the buttermilk and cheddar until just incorporated.
For the Chili:
In a large, heavy ovenproof skillet, heat oil over medium-high heat. Add bell pepper and onions. Cooking, stirring, until tender, 8 to 10 minutes.
Add the turkey, tomato paste, and chili powder to skillet and cook until the meat is no longer pink.
Add the diced tomatoes (with liquid) and cook until the liquid has reduced, about 3 minutes. Season with salt and pepper. Remove from heat.
Putting it all together:
Take 3 tablespoon size scoops of the batter and place it on top of the chili. Bake in the oven until the biscuits are golden brown, about 20 minutes.