Preheat oven to 400 degrees. Lightly butter an 8-inch square baking dish.
Trim fennel bulbs; halve, and core. Slice bulbs and potatoes very thin (1/8 inch thick).
Add potatoes to prepared dish in three layers, alternating with two layers of fennel; season each layer with salt and pepper, sprinkle with 2 tablespoons Asiago, and dot with 1/2 tablespoon butter. (Omit cheese from final layer.)
Pour cream over top. Bake until potatoes are tender when pierced with the tip of a paring knife, about 45 minutes. Sprinkle with remaining 1/2 cup grated Asiago; bake until golden brown, 15 to 20 minutes.