1 pound fresh mushrooms, sliced
2 tablespoons extra-virgin olive oil
2 tablespoons butter (may substitute 2 additional tablespoons olive oil)
1 tablespoon Worcestershire sauce (or more to taste)
About 1/4 teaspoon Tabasco sauce
2 tablespoons balsamic vinegar
Salt and white pepper, to taste
8 ounces traditional feta, drained and crumbled
8 ounces shredded extra-sharp cheddar (preferably Tillamook)
1/3 cup grated Parmesan
2 cups half-and-half
In a very large skillet, saute the mushrooms in the olive oil and butter over medium-high heat until mushrooms have released their liquid, then continue cooking until liquid has reduced and mushrooms are getting very golden-brown, shaking and stirring so they all get evenly cooked.
Drizzle on the Worcestershire and Tabasco sauces and continue stirring, scraping and sauteing until sauce has reduced and mushrooms are even more golden. Add the balsamic vinegar and continue to saute and stir until vinegar has reduced and mushrooms are very brown. Sprinkle with the salt and pepper.
Spread sauteed mushrooms in bottom of an 11-by-17-inch baking pan. This will make only a shallow layer. Sprinkle on the feta, shredded cheddar and Parmesan cheeses. With your fingers, toss some mushrooms with cheese, so bits of cheese are snuggled within and beneath mushroom layer.
In a bowl, whisk together the eggs, half-and-half, scant 1/2 teaspoon salt and a pinch of pepper. Ladle enough of this mixture over mushrooms and cheese so it is evenly immersed, with pieces of mushroom and cheese still poking out top (in other words, don't completely cover mushrooms with custard; you may have some custard left over).
May prepare gratin up to this point and refrigerate for up to 24 hours.
Bake gratin in a 400-degree oven until top is golden and custard tests firm when pressed with your finger, about 25 to 30 minutes. Remove from oven. Makes 8 to 10 servings.