1. Heat 2 tablespoons oil in a large nonstick skillet over moderately high heat. Add mushrooms and cook in 3 batches, stirring occasionally, until liquid evaporates, about 5 minutes per batch (add more oil between batches if needed). Transfer mushrooms with a slotted spoon, as cooked, to a large bowl. Heat 1 tablespoon oil in skillet over moderately high heat. Add onion and thyme; cook, stirring occasionally, until golden, about 15 minutes. Transfer to bowl with mushrooms. Wipe skillet clean and heat 1 tablespoon oil over moderately high heat; add bread crumbs and cook, stirring, until golden, about 2 minutes.
2. Preheat oven to 400 degree F and lightly oil a 3-1/2-quart casserole dish. Cook orzo in a 6-quart pot of boiling salted water until al dente. Transfer 2 cups pasta water to a medium bowl. Drain pasta in a fine-mesh colander and transfer to bowl with mushrooms; combine. Whisk goat cheese into pasta water and stir into pasta mixture with spinach; season with salt and pepper. Spoon orzo mixture into prepared dish and sprinkle top with bread crumbs. Bake in middle of oven until heated through and crumbs are golden brown, about 20 minutes. Makes 6 to 8 servings.