Sauté veggies. Heat butter in a large stockpot over medium-high heat. Add mushrooms and sauté, stirring occasionally, for 5-7 minutes or until most of their liquid has evaporated and the mushrooms are browned. Add onion and sauté for 3 minutes, stirring occasionally. Add garlic and sauté for 2 minutes, stirring occasionally.
Cook the pasta. Add pasta, water, half and half, Dijon, crushed red pepper flakes, a generous pinch of salt and pepper and stir to combine. Bring the pasta to a boil, stirring occasionally to break up the pasta. Once the pasta reaches a boil, stir in the broccoli. Reduce heat to medium to maintain a low boil and continue cooking the pasta uncovered until it is just al dente.
Remove excess liquid (if needed). Check to see how much liquid remains in the pot. If it seems that there is more than ½ cup or so, dip a heatproof measuring cup in to remove and save the excess liquid, and set it to the side.
Add cheese. Stir in the cheeses until melted and combined. If the pasta seems too dry, stir some of the reserved liquid back in as needed.
Season. Taste and season with additional salt and pepper as needed.
Serve. Serve warm and enjoy!
Notes
Pasta shape: As noted above, I wrote this recipe using a pasta shape that lists a 7- to 8ish-minute cooking time. But if the pasta shape that you have on hand requires more or less cooking time, no worries, just add or subtract pasta cooking water as needed. (See explanation detailed in the blog post above. You should only have about 1/2 cup of starchy pasta water remaining in the pot, removing any extra, before mixing in the cheese.)