A “gratin” is a dish topped with either some cheese or a breadcrumb mixture and finished under the broiler. Think yummy golden brown topping!
Preheat oven to 350 degrees F.
Cut bulb of fennel in half, lengthwise. Slice each half into 6 wedges and trim core. Leave a little of the core intact to keep fennel together. Place fennel into medium saucepan and pour in stock. Season with salt and pepper. Bring to a boil over high heat. Cover and reduce heat to medium. Braise fennel until just tender, about 10 minutes. Drain liquid and save for soup, if desired.
Brush an 8×10-inch shallow baking dish with olive oil. Sprinkle bottom of baking dish evenly with sliced shallots. Lay fennel over top shallots in a single layer. Arrange endive on top of fennel in a single layer. Season with salt and pepper. Cover with foil, bake for 10 to 12 minutes or until endive just begins to steam.
Meanwhile, make the béchamel. Melt butter in a medium saucepan over medium heat. Add the flour and stir with a wooden spoon to combine. Remove pan from heat and whisk in cold milk in a steady stream. Continue to whisk until smooth. Return pan to heat over medium heat. Stir until mixture thickens and begins to boil. Season the béchamel with salt and pepper and nutmeg. Stir in the crumbled goat cheese. Removed from heat.
Preheat broiler to high.
Pour the béchamel sauce over top of fennel and endive mixture, spreading evenly to cover. Broil or until golden and bubbly, about 3 to 5 minutes.