In a large soup pot or dutch oven, melt the butter over low heat.
Add the onion and garlic. Saute 2 to 3 minutes. Stir in the flour and cook another 2 minutes, constantly stirring to mix the flour in with the butter and coating the onions with a paste.
Slowly whisk in 1 cup of the veggie broth, using the whisk to break up and dissolve any clumps of flour mixture. Add all of the remaining broth to the pot. Continue heating and stirring until all of the flour mixture has dissolved into the broth.
Add all of the remaining ingredients to the pot.
Turn up heat to medium high until the soup boils. Cover and reduce heat to low and let simmer 30 to 35 minutes, or until the rice is tender and fully cooked.