Heat a large pot over medium-high heat. Spritz with cooking spray, then add the onion. Sauté until onions are just soft, about 2-3 minutes. Add garlic and cook for another 30 seconds, stirring constantly.
Add chicken stock to the pot. In a separate bowl, whisk together almond milk, half and half, and cornstarch. Add this mixture to the pot and bring to a boil.
When liquid is boiling, mix in broccoli, carrots, dijon, nutmeg, salt, and pepper. Cover pot and lower to a mild simmer (around low-medium heat).
Simmer for about 20 minutes. Remove lid, turn off heat, and whisk in cheese, a handful at a time, to avoid clumping.
Whisk cheese, a handful at a time, into the soup until melted. Continue with all of the cheese.
Let soup stand for about 5 minutes, to thicken up.