Roast brussels sprouts and cook fettucine. Preheat oven to 400 F and put a pan of water on to boil Cut off the ends, then slice them in half length wise. Lay them flat side down on a baking sheet, drizzle with olive oil and salt. If you toss them too much they’ll fall apart, so just kind of move them around with your hands until they’re coated in oil. Roast them for 20 minutes, or until browned on the bottoms and around the edges. Set aside. When the water is boiling, add the pasta and cook according to package directions.
Cook prosciutto. While the brussels sprouts are roasting and the fettucine is boiling, heat a nonstick pan over medium-high heat. Rip the prosciutto into pieces with your hands and drop them into the pan. Cook, stirring occasionally, for 5 minutes, or until desired doneness. Set aside.
Make sauce. In the same nonstick pan you used to cook the prosciutto, melt the butter. Let it come to a bit of a bubble, then add garlic, nutmeg, white pepper, and salt. Let it all cook, stirring here and there, until the garlic is fragrant and the butter is browning. (You’re not watching for the liquid to brown—just the little bits floating around the bottom.) Once the butter is browning, immediately add the cream. Stir well, but don’t worry if the oil doesn’t incorporated well at first. It will. Bring the cream to almost a boil, then turn down the heat and let it simmer for 8-10 minutes, whisking pretty frequently, until it has thickened. Take it off the heat and add the parmesan a little at a time, whisking to incorporate it fully before adding more. It can be hard to make the sauce totally smooth, so don’t worry if you can’t. A quick blitz in the blender or with an immersion blender will fix that.
Toss it all together. Toss the cooked fettucine with ¾of the sauce (reserve the other ¼ for freshening up leftovers), roasted brussels sprouts, and prosciutto.