To make the pasta, fill a large pot with 2 inches (5 cm) of water, enough to fully submerge the pasta, cover, and bring to a boil. Once it’s boiling, add the pasta, cover, and bring to a boil again. Once it’s boiling, you can remove the lid and continue to cook until al dente, according to the package directions. Drain the pasta.
Cook the broccoli florets by adding them to a large pan along with the water, then cover and bring to a boil. Reduce the heat and let the broccoli cook until it’s bright green and fork tender, 8 to 10 minutes depending on the size.
Meanwhile, prepare the sauce. Place a medium-sized saucepan over medium heat and add the butter. When the butter melts, add the flour and whisk until combined. Then slowly drizzle in the oat milk, whisking constantly as you pour. Add the coconut milk, salt, pepper, garlic powder, and onion powder. Stir and let the sauce continue to cook for 1 to 2 minutes to reach a simmer, then stir in the plant-based cheddar and mozzarella. Let the sauce cook for 1 to 2 minutes as the cheese melts, then whisk in the mustard and nutritional yeast.
Finely chop the fresh parsley. Combine the cooked pasta with the sauce, sun-dried tomatoes, broccoli, and fresh parsley. Serve topped with red chili flakes.