First begin by sautéing the vegetables. In a large saucepan over medium heat, melt the butter. Add the onion and sauté until translucent, 3 to 4 minutes. Add the carrots, celery and thyme leaves and sauté until the vegetables are softened, about 3 minutes more. Add the stock, increase the heat to medium-high and simmer for 5 minutes to blend the flavors.
Add the pasta to the simmering soup and cook until the pasta is al dente, 3 to 4 minutes, or according to the package instructions. Add the spinach and chicken and cook, stirring, until the spinach has wilted and the chicken is warmed through, about 1 minute. Season to taste with salt and pepper.
Ladle the soup into warm bowls and garnish with some of the cheese. Serve immediately with remaining cheese at the table.