Heat a large sauté pan or skillet, and sear filet mignon in a bit of oil before going on to next step. Reduce heat to medium. The filet is optional.
Add butter to the sauté pan. Over medium heat, sauté onion until golden; add shallot and garlic. Gently stir in mushrooms for 3 minutes or until onions turn golden brown. Add red wine and 11/2 cups hot vegetable stock, scraping bottom of skillet. Add salt and pepper to taste, and minced herbs. Remove from heat and let stand, covered, for 20 minutes. Pour hot liquid into a large glass measuring cup.
In a large skillet, make a brown butter roux with 3 tablespoons butter, and 3 tablespoons sifted flour. Slowly pour in hot mushroom liquid after the flour has turned beige. Whisk until smooth, and cook for 3 to 5 minutes. Fold in mushroom mixture and remove from heat.
Preheat oven at 375 degrees.
In a large saucepan, boil 4 cups water, 2 cups vegetable stock, 1/2 tablespoon plain salt, and 3 tablespoons olive oil or butter. Stir polenta into the water gradually with a wooden spoon or spurtle, and boil gently. Stir constantly until thickened, about 10 minutes. Remove from the heat, and stir in 1 cup grated Romano or Parmesan cheese.
Place the mushroom mixture in 6 individual ramekins sprayed with nonstick spray. Add a layer of mozzarella. Heap loose, hot polenta on top. Sprinkle with Parmesan or Romano, and place on a baking sheet. Bake until polenta is golden and mushroom filling bubbles, about 20 minutes.
Garnish with shaved Parmesan or Romano, and fresh herbs. Serve immediately.