Preheat oven to 450°. Pour oil into a 12- by 17-in. rimmed baking pan and lightly oil with a paper towel. Sprinkle pan with cornmeal.
On a lightly floured surface, stretch dough with hands and/or roll with a rolling pin into a rectangle roughly the same size as the pan. Transfer dough to pan, stretching to fit. Fold over 1/2 in. of dough around edges to form a slightly raised rim for the tart. Prick dough all over with a fork.
Heat a large frying pan over high heat. When hot, add olive oil and swirl to coat. Add mushrooms and thyme; sprinkle with salt and freshly ground black pepper. Cook mushrooms, stirring, until they stop giving off liquid and start to brown. Add chopped onions, reduce heat to medium-high, and cook, stirring until onions are softened, about 4 minutes. Scatter mushrooms and onions over tart dough, then sprinkle cheese evenly on top.
Bake tart until cheese is melted and beginning to brown and crust is crisp and well browned, 20 to 25 minutes. Lift out of pan with a spatula, cut into roughly 2-in. squares, and serve immediately.
Make ahead: The tart can be made up to 2 days ahead and kept wrapped in waxed paper at room temperature. To serve, unwrap and reheat 10 minutes at 200°.
Note: Nutritional analysis is per hors d'oeuvre.