Heat 2 tablespoons of vegetable oil in a large pot over medium-high heat.
Season the chicken breasts with salt, pepper, and garlic powder. Add them to the pot and cook for 3-4 minutes per side until cooked through.
Brush 2 tablespoons of barbecue sauce over each chicken breast as they finish cooking. Remove the chicken from the pot and set aside.
Add diced onions to the pot (with an extra drizzle of oil, if necessary) and cook until softened. Stir in the minced garlic and cook for about 1 minute.
Pour in the can of diced tomatoes (with juices) and chicken stock. Stir to combine, then mix in the uncooked rotini pasta and cooked chicken (chopped into 1-inch chunks).
Bring the mixture to a boil, cover the pot, and reduce the heat to medium. Let it simmer for 12-15 minutes, stirring occasionally, until the pasta is tender.
Turn off the heat, stir in 1/4 cup of additional BBQ sauce, and sprinkle the cheddar cheese on top. Cover the pot for a couple of minutes to let the cheese melt. Serve hot!