Instructions: 

1. Melt butter in a small saucepan, stirring frequently, over medium-low heat. Continue to cook the butter until brown bits form at the bottom of the pan, about 6-8 minutes. Once the butter is browned, remove it from heat.
2. Cook pasta in a large pot of boiling water, stirring occasionally, until al dente, about 8-10 minutes. Drain, reserving 1 cup pasta water, and set aside.
3. While the pasta cooks, heat olive oil in a large skillet over medium-high heat. Swirl to coat the bottom and then add in shallot, Brussels sprouts, red pepper flakes, salt & pepper. Sauté until Brussels sprouts are tender and caramelized, about 6-8 minutes. 
4. Add lemon juice, Parmesan and pasta to the pan. Pour in brown butter and add about 1/3 cup of the pasta water, 1 Tbsp. at a time, stirring constantly, until sauce reaches desired consistency. Toss until pasta is coated well in sauce.
5. Divide pasta into serving dishes and garnish with walnuts and Parmesan. Serve and enjoy!