Set an oven rack about 6 inches from the heat source and preheat the oven’s broiler. Lightly grease a baking dish.

Bring a large pot of lightly salted water to a boil over medium-high heat. Add endive; cover and cook until tender, 5 to 10 minutes. Drain.

Melt butter in a saucepan over medium heat. Whisk in flour until paste-like and golden brown. Gradually whisk in milk, whisking constantly until thick and smooth. Stir in 3/4 cup Gruyère cheese, Parmesan cheese, nutmeg, salt, and black pepper until combined. Reduce heat to medium-low; cook gently for 10 minutes, stirring frequently.

Wrap each endive with 1 slice ham; place into the prepared baking dish. Pour cheese sauce over top; sprinkle with remaining 1/4 cup Gruyère cheese and parsley.

Cook in the preheated broiler until cheese is golden brown and sauce bubbles, about 10 minutes.