Heat a large skillet over medium heat. Add the ground turkey sausage, crumble with a spatula, and cook until browned and nearly cooked through, about 5–8 minutes.
Drain excess fat from the skillet if needed, leaving a thin film for flavor.
Add the diced onion and sliced mushrooms to the skillet along with the Italian seasoning, kosher salt, and tomato paste. Cook, stirring occasionally, until the onion is softened and mushrooms are cooked, about 5–6 minutes.
Stir in the chopped spinach and diced tomatoes. Bring the mixture to a gentle simmer, then cover and cook 2–3 minutes until the spinach is wilted and everything is heated through.
Add the precooked quinoa to the skillet and toss until evenly combined and heated through.
Divide the quinoa mixture into bowls and top with shredded Parmesan and red chili flakes to taste.