Heat olive oil in a large high-rimmed sauté pan over medium-high heat. Add the chicken sausage (casing removed). Use a spoon or spatula to break the sausage into crumbles. Cook for about 5 minutes to get some color and partially cook the sausage.
Add the red pepper flakes, umami seasoning, salt, pepper, fresh thyme leaves, shaved Brussels sprouts, and garlic. Stir to combine and cook for about 5 minutes, stirring occasionally. Add an additional splash of olive oil if the pan is too dry. Mix in the zest and juice of 1/2 a lemon and cook for another 2 minutes.
Meanwhile, cook pasta in salted water to al dente according to package instructions. Transfer directly over to the sausage mixture once cooked. Add the grated parmesan cheese and 1/2 cup of pasta water. Combine well and add another 1/2 cup of pasta water as needed to create a sauce. Season to taste with additional salt and pepper as needed.
Divide among bowls to serve. Top with additional lemon juice, parmesan cheese, and a drizzle of olive oil as desired.