Rinse the mushrooms to remove any dirt or debris, then slice them thinly. Mince the garlic.
Melt the butter in a large skillet over medium heat. Add the garlic and sauté for 1-2 minutes or just until soft and fragrant. Add the sliced mushrooms and continue to sauté until they are soft, dark, and all of the moisture they release has evaporated (5 minutes).
Make sure that all of the moisture released by the mushrooms has evaporated and just the butter oil and mushrooms remain in the pan. Turn the heat down to medium-low, add the flour, and continue to sauté the flour with the mushrooms and butter. The flour will form a paste like mixture all over the mushrooms and eventually begin to coat the bottom of the skillet. Continue to sauté for 3-4 minutes, or just until the flour begins to turn golden brown on the bottom of the skillet. This will slightly toast the flour and give the gravy better flavor.
Slowly whisk in the vegetable broth. Whisk well to make sure that all of the flour has dissolved off the bottom of the skillet and no lumps remain. Add the sprigs of thyme, sage, and some freshly cracked pepper. Stir to combine.
Allow the mixture to come to a simmer. The gravy will begin to thicken as soon as it simmers. Allow the gravy to simmer for 7-10 minutes, whisking often, until it is the desired thickness. Remember that the gravy will continue to thicken as it cools. Taste the gravy and adjust salt and pepper to your liking.