Cook pasta according to package instructions. Drain and set aside.
While pasta is cooking, heat olive oil in a pan over medium-high heat. Add shallot, brussels sprouts and salt & pepper (to taste). Saute until shallots become translucent and brussels sprouts begin to brown, stirring frequently. Using a slotted spoon, place the veggies on a plate and set aside.
Place pan back on the stove and lower heat to medium. Add butter, garlic, milk, veggie broth and flour to the pan. Whisk until flour is incorporated. Simmer on low for 5 minutes to allow sauce to thicken. Add salt & pepper and stir to combine. Taste and adjust seasoning as needed. Remove from heat.
Add drained pasta to the sauce and stir to combine. Top pasta with brussels sprouts and shallot and serve!