Bring a large pot of salted water to a boil. Add linguine pasta to water and cook until al dente, according to package directions.
Meanwhile, heat olive oil in a large non-stick skillet over medium heat. Add diced carrots to heated oil. Cook and stir for 5 minutes or until carrots are softened. Add broccoli and zucchini to skillet. Stir and cook another 3 minutes. Then add all the bell peppers. Continue to cook and stir vegetables for another 5 minutes. Stir in minced garlic and basil paste (or fresh basil). Stir to combine and season with salt and pepper. Turn heat off and remove skillet from burner.
Drain water from linguine. Return linguine back to the pot and add the cooked vegetables, heavy cream and Parmesan cheese. Carefully fold and stir to combine everything. Season again with salt and pepper. Serve warm with extra basil and Parmesan cheese. Enjoy!