In a medium-sized bowl or measuring cup, whisk together the gluten free flour into 2 cups of the vegetable broth. Set aside to use in a few minutes.
In a large pot, heat the olive oil over medium heat and add in the onion. Cook the onion until soft and translucent, then add in the garlic and cook for an additional minute.
Add the vegetable broth containing the gluten free flour into the pot, along with the remaining 4 cups of broth, salt and pepper. Continue to heat the soup for about 5 minutes, until the mixture starts to thicken. To prevent clumping, stir the broth frequently. If clumps do appear, whisk the broth (carefully) to break them apart.
Add the broccoli and carrots into the pot and set the heat to high. Cover the pot and bring the soup to a boil - then simmer for about 15 minutes, or until the broccoli is tender. (Use a fork to lightly pierce the broccoli.)
Remove the soup from heat and then mix in the cheese. Stir until melted and serve.
