Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Cook pasta in boiling water, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain well in a colander set in the sink.

Heat olive oil in a skillet over medium heat. Stir in zucchinis, bell pepper, carrots, mushrooms, and onions; cook and stir until onions are softened and translucent, about 5 minutes. Add garlic and cook for 1 minute more. Stir in tomatoes, chicken broth, parsley, basil, oregano, and red pepper flakes.

Bring to a boil, then reduce heat to low and simmer until sauce thickens. Stir in pasta and cook until heated through, about 2 minutes. Top with Parmesan and Gouda cheeses to serve.