Position a rack in the top third of the oven, put a large heavy-duty rimmed baking sheet on the rack, and heat the oven to 500°F.
Trim the fennel, quarter each bulb vertically, and trim away most of the core, leaving just enough to hold the layers intact. Slice each quarter into 4 wedges.
In a medium bowl, toss the fennel with the olive oil, 1/2 tsp. salt, and 1/2 tsp. pepper. Remove the baking sheet from the oven and quickly spread the fennel on the sheet, with the largest pieces toward the edges of the pan. Roast until the fennel pieces are almost tender and the bottoms are lightly browned, about 18 minutes.
Flip the fennel, sprinkle with the thyme and then the Asiago, and continue roasting until the cheese is melted and golden, 3 to 5 minutes more. With a spatula, transfer the fennel and any lacy, golden cheese bits to a serving dish.
Turn this side dish into a hearty main by tossing the roasted fennel with pasta and topping it with garlicky toasted breadcrumbs.