Preheat the oven to 350°. Bring a large pot of salted water to a boil. Add the fennel and cook until crisp-tender, about 10 minutes. Drain and pat dry.
In a medium saucepan, melt the butter. Add the garlic and cook over moderate heat until softened, 2 minutes. Add the cream and cook until reduced to 2 cups, about 20 minutes. Off the heat, whisk in 1 cup of the cheese. Gradually add the eggs and whisk until incorporated. Transfer the sauce to a blender and puree until smooth. Season with salt and white pepper.
In a small bowl, mix the bread crumbs with the parsley and the remaining 1/2 cup of cheese. Season the bread crumb mixture lightly with salt and white pepper.
Arrange the fennel in a single layer in a 9-by-13-inch baking dish. Pour the cream sauce over the fennel, sprinkle with the bread crumb mixture and drizzle with the olive oil. Bake for about 45 minutes, until the fennel is tender, the sauce is bubbling and the crumbs are browned on top. Let stand for 15 minutes before serving.
The assembled gratin can be refrigerated overnight. Bring to room temperature before baking.