1/4 cup chicken or turkey stock or canned low-sodium broth
In a saucepan, steam the fennel, root end up, until just tender, about 15 minutes. Let cool. Halve the bulbs lengthwise and remove the thickest part of the core.
Heat 2 tablespoons of the oil in a large skillet. Add the sausage, breaking it up with a wooden spoon, and cook over moderately high heat until no pink remains, 5 minutes. Add the onion and garlic. Cook, stirring occasionally, until the onion is softened and the sausage is browned, 5 minutes. Stir in the bread crumbs. Let cool. Stir in the cheese and parsley; season with salt and pepper.
Preheat the oven to 425°. Oil a large glass baking dish; pour in the stock. Working over the skillet, press two-thirds of the filling into the fennel layers. Arrange the fennel in the baking dish, cut side up, and top with the remaining filling. Tilt the fennel up slightly and drizzle 1/4 cup of olive oil over and between the layers. Cover loosely with foil and bake for 20 minutes, or until the fennel is very tender. Uncover and bake for 10 to 15 minutes longer, or until the liquid in the dish has evaporated and the fennel begins to brown on the bottom.
Position an oven rack 10 inches from the heat and preheat the broiler. Broil the fennel until the topping is browned, about 5 minutes. Serve hot.
The recipe can be prepared through Step 3 early in the day. Rewarm and broil before serving.