1. In a large pot of boiling, salted water, cook the pasta following the package instructions until al dente. Drain the pasta, reserving 1 cup of pasta water for the sauce. Transfer the pasta to a rimmed baking sheet, untangling the pasta so it lies flat (and cools quickly).

2. In a large skillet set over medium-high heat, melt the butter. Once the butter is melted, increase the heat to high, then add the Brussels sprouts and cook until golden brown and just barely tender, about 4 minutes. Stir in the garlic, shallot and red pepper flakes, season with salt and pepper, and cook until the garlic is fragrant, about 1 minute.

3. Pour in the reserved pasta water and shake the pan to incorporate the butter and vegetables. Add the pasta; using tongs, toss it with the sauce. Turn off the heat and mix in the Parmesan cheese and lemon juice. Taste and add more salt or pepper if needed. Stir in the parsley and serve.