In a large stock pot, add the oil and butter along with the pearl onions and carrot slices. Saute for a few minutes until tender. Add garlic (if using). Saute 1 minute more.
Add the flour and tomato puree, cooking for 1 minute. Add wine.
Next, combine the boiling water and Better Than Bouillon NO BEEF Base until dissolved. Add to stock pot.
If you'd like to add fresh thyme leaves, do so now.
Meanwhile, in a large skillet, add oil and mushrooms over high heat. Stir frequently for just a few minutes until tender.