Clean truffles and cèpes by wiping with a damp cloth. Set truffles aside. Separate cèpe stems from caps with a paring knife and remove and discard spongy underpart of caps if soft. Peel stems and cut into ¼"-thick slices. Cut caps into quarters or sixths depending upon size.
For sauce, heat 2 tbsp. oil in a large skillet over medium heat. Add 5 cloves of garlic and cook, stirring frequently, for 2 minutes. Add cèpe stems and cook until tender, about 5 minutes.
Transfer garlic and stems to a food processor, add stock, and purée until smooth. Strain through a fine sieve into a small saucepan. Simmer over medium-high heat until reduced by half, 7–10 minutes. Cover and keep warm over low heat.
Wipe out large skillet and heat remaining oil over medium-high heat. Add cèpe caps and remaining garlic and sauté for 3 minutes, then add 4 sprigs thyme, season with salt and pepper, and cook, stirring occasionally, until caps are golden, about 3 minutes.
Using a vegetable peeler thinly shave truffles into skillet, toss with cèpes, and cook just until heated through, about 1 minute. Whisk butter into sauce, and season with salt and pepper. Discard sautéed garlic and thyme, spoon cèpe and truffles onto plates, surround with sauce, and garnish with fresh thyme. Serve immediately.