In a 3-quart pot add onion, carrot, celery, water, chicken bouillon, beef bouillon, thyme, rosemary, and black pepper. Bring to a boil and simmer for 20 minutes. Stirring occasionally.
In a small bowl, use a fork to mix the gluten-free flour and butter.
Use a slotted spoon and strain out the vegetables.
Add about ⅓ of the gluten-free flour mixture into the hot water. Use a whisk to break up any lumps of flour. Continue this process until all of the flour mixture has been added and there are no more lumps.
Heat the gravy until it begins to bubble and continue cooking for 1-2 minutes. The gravy should begin to thicken.
Salt to taste.
Serve.