In a large skillet, heat olive oil until hot. Add the sausage and cook 5 minutes or so, until browned on all sides.
Add carrots and peppers to the sausage and cook stirring often for 2 – 3 minutes Add the garlic and cook 1 minute more until ii is fragrent. Be careful to not let the garlic burn.
Stir in the remaining ingredients into the pan and bring to a boil. Reduce the heat to low and simmer approximately 15 minutes. The soup should thicken slightly and the sausage should be cooked through completely.
Serve with a generous sprinkling of Peccorino Romano cheese.