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Preheat oven to 450 degrees.
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Boil 3 fennel bulbs, trimmed and split lengthwise, until tender, about 15 minutes. Drain fennel, cut side down, on paper towels, 5 minutes.
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Place fennel, cut side up, in a buttered 8-inch square baking dish and brush with 1 tablespoon softened butter.
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Season with coarse salt and ground pepper and top with 1/3 cup grated Parmesan and 4 sprigs thyme.
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Bake until cheese is golden brown, about 20 minutes.