Heat 1 tablespoon olive oil in a large Dutch oven or soup pot over medium-high heat until shimmering but not smoking. Add chopped chicken breasts and cook until they are almost cooked through, about 5-7 minutes, stirring occasionally to ensure even cooking. Once done, transfer the chicken onto a plate and set aside.

In the same pot, melt 3 tablespoons of butter along with the remaining 2 tablespoons of olive oil over medium-high heat until bubbling slightly but not burning. Add chopped onions and sliced carrots to the pot; sauté them together while stirring continuously for about 3 minutes until softened slightly before adding in the bell pepper and minced garlic.

Sprinkle in 1/3 cup flour into the vegetable mixture while continuously stirring to create a roux-like consistency, cooking it down for another 3 minutes until it becomes thickened but not browned.

Lower the heat setting to medium-low before gradually pouring in approximately 8 cups of low sodium chicken broth while whisking constantly to avoid lumps from forming in your soup base; then whisk together 3 tablespoons cornstarch with an additional cup of broth before adding it into your mixture.