Bring a pot of water to boil and fit it with a steamer attachment. Steam the carrots till they're tender, about 8 minutes. Alternately, you can place the carrots in a microwave-safe bowl with 2 tablespoons water and microwave for 4 minutes, or until they're tender. Set the carrots aside.
Bring a larger pot of water to boil. Add the pasta and cook according to package instructions; 2 minutes before the cooking time is up, add your Brussels sprouts or other vegetable to the pot.
While the water boils and/or pasta cooks, transfer the cashews, cooked carrots, 3/4 cup water, salt, lemon juice, nutritional yeast, and garlic to a powerful blender or a food processor. Blend till the sauce is very smooth; if it's very thick or it won't blend nicely, add an extra 1-3 tablespoons water, or as much as you need to get a thick but smooth and pourable mixture. Add black pepper to taste.
To make the parm, transfer all ingredients to a food processor and pulse till you have a fine crumble. (This can be done in advance; the parmesan will keep for up to 2 weeks in an airtight container in the fridge.)
When the pasta and veggies are ready, drain them. Add the sauce and mix well; taste, then add additional salt as needed. Divide the mac onto plates and top with the walnut parm or your vegan parm of choice. Serve.
The carrot sauce can be prepared up to four days in advance and stored in an airtight container in the fridge.