Rinse Belgian endive; trim off any discolored bases. Cut heads in half lengthwise. Arrange the halves, cut side down, in a single layer in a heavy 11- to 12-inch frying pan. Add 1/4 cup water and the olive oil. Sprinkle endive lightly with salt and pepper. Cover pan and bring to boil over high heat, then reduce heat and simmer until endive is very tender when pierced, 12 to 20 minutes. Uncover and cook over medium heat, turning heads occasionally, until liquid is evaporated and endive is slightly browned, 6 to 10 minutes.
Meanwhile, in a 1- to 2-quart pan over medium-low heat, melt butter. Stir in flour until blended and bubbly. Add milk and nutmeg; stir until mixture is boiling and thickened, about 10 minutes. Stir in 1/2 cup cheese. Add salt and pepper to taste.
Arrange endive in a single layer in a shallow 2-quart baking dish. Spoon sauce over the top. Sprinkle evenly with remaining 1/4 cup cheese.
Bake, uncovered, in a 400° oven until sauce is bubbling and lightly browned, 9 to 14 minutes. Add more salt and pepper to taste.