In a pot with a lid, combine the broth, onion, broccoli, carrots, garlic, bay leaf and some garlic salt and pepper. Bring the mixture to a boil and then reduce the heat to medium-low and place the lid on the pot. Simmer for about 15 minutes or until the broccoli is nearly cooked through.
When the veggies are nearly done, melt the butter over medium heat in a large Dutch oven. Whisk in the flour and let it cook for a couple minutes. Once the broccoli mixture is cooked, begin adding the liquid you cooked the vegetables in to the Dutch oven with a ladle, whisking as you do to incorporate the flour roux.
Once the liquid thickens a bit, toss in the vegetables (remove the bay leaf), milk and more garlic salt and pepper, if desired.
After the mixture is heated through, remove it from the stove and stir in the cheese until it's melted.
Serve with some crusty bread and a fresh salad to really bring in the garden-fresh deliciousness.