Preheat oven to 425ºF. Add the chopped carrots and onion to a baking sheet and toss with the olive oil. Bake for 15 minutes before flipping and baking another 15 minutes. With 5 minutes left add the garlic so it doesn't burn.
Add the roasted veggies to a blender with the veggie broth, tomato paste, balsamic vinegar, salt, pepper and crushed red pepper flakes. Blend until smooth.
Bring a large pot of salted water to a boil and cook the pasta al dente according to package instructions. Save ½ cup of pasta water
Add the sauce, penne and cheese to a large skillet, tossing to combine. Pour in ¼ cup of reserved pasta water and toss together. Taste and adjust seasoning. Serve with some parsley and cheese on top.
Notes
You control the amount of heat, so if you like it spicier, increase the crushed red pepper flakes by ¼ teaspoon until you like the spice level. If you want it less spicy reduce the amount by ¼ teaspoon at a time.
Make sure the water you are cooking the pasta in is salted as some of the flavor comes from it.
DO NOT overcook the pasta when boiling. You want it just al dente or slightly under. It continues to cook with the sauce.
Thin the sauce as needed. If the sauce is too thick, use some of the pasta water to get to your liking.
Don't use pre-shredded cheese. You want if finely grated so it melts well. Pre-shredded has added ingredients that will just make it clump up.
If you want some protein, pancetta or Italian sausage are great options.