Heat oil and butter in a large skillet over medium-low heat until melted. Add shallots and cook, stirring frequently, until translucent. Add garlic and cook until fragrant, about 1 minute.
Add mushrooms, thyme, salt, and pepper and cook, stirring frequently, until mushrooms are cooked through and all liquid has evaporated, about 15 minutes. The duxelle should be quite dry.
Tofu
Cut tofu in half crosswise. Then cut on a diagonal to create 4 pieces.Cut a slit into the tofu along the longer side of the triangle.
Stuff each triangle with mushroom duxelles. Set aside remaining duxelles for the gravy.
Place flour, beaten egg, and breadcrumbs in separate wide bowls.
Dredge tofu in flour, then egg, then breadcrumbs, carefully coating each side.
Place coated tofu on a plate and refrigerate for 15 minutes to set breading.
Heat oil and butter in a large skillet over medium heat, until the oil/butter is shimmering.
Gently place tofu in oil and cook until browned. Turn and continue to cook all sides until browned.
Mushroom Gravy
Place the remaining duxelles in a large skillet. Make a well in the center and place butter in center. Melt butter and add flour on top. Stir for 2 minutes.
Add water or broth, salt, and pepper and stir vigorously. Simmer until the gravy is thickened.
Recipe by The Gardener Cook at https://www.thegardenercook.com/stuffed-tofu-with-mushroom-duxelles-and-gravy/