Soak mushrooms in 1 cup of hot water until tender, about 5 minutes. Strain through a paper to remove any grit. Reserve liquid and place mushrooms in a food processor along with carrots, celery, onion and thyme. Pulse veggies until finely chopped.
In a Dutch oven, melted butter then add minced veggies, sautéing for 5 minutes. Add wine and reserved mushroom liquid, bring to a simmer allowing to reduce by half.
Add tomatoes, and simmer until sauce thickens, about 10 minutes. For a saucier consistency you can add 1-2 tablespoons of tomato paste.
Just before serving stir in basil and season to taste with salt and pepper, then toss with your favorite gluten free pasta.