Bring a large pot of lightly salted water to a boil for pasta.

Meanwhile, heat olive oil over medium-high heat in a deep skillet. Add onion and garlic to the hot oil and saute just until tender, about 5 minutes. Add kielbasa to the skillet and cook and stir until browned, 3 to 4 minutes. Stir in tomatoes, mushrooms, sugar, balsamic, salt, black pepper, and red pepper. Reduce heat and let sauce simmer while you cook pasta.

Add penne to the pot of boiling water and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes, stirring peas into pasta during last 2 minutes of cooking time.

Drain pasta and transfer to sauce. Stir to combine and add basil. Heat over medium-low heat so pasta can absorb liquid from sauce, about 5 minutes. Stir in Cheddar-Monterey Jack cheese and serve.