In a large pot, over medium-high heat, add the vegetable stock, the chopped broccoli, carrots, onion, garlic and bay leaves. Stir and cook for about 20 min the veggies need to be tender. Remove the bay leaves.
In a separate large pot, melt the 6 butter over medium heat. Slowly whisk in the flour creating a paste, and cook until just starts to brown. Pour in the broth and veggies, and mix well. Stir in the 2 cups of half and half and stir to combine mixture. Sprinkle in the garlic salt, nutmeg, basil and cayenne.