Preheat the oven to 350°F (175°C). Arrange a rack in the middle of the oven. Grease a 9-by 13-inch baking dish with a bit of the butter.

Halve each endive lengthwise, through the root.

Melt the butter in a large skillet or sauté pan over medium heat. Place the endive, cut-side down, in a single layer. Let cook, undisturbed, until golden, 3 to 4 minutes. Add the chicken broth and bring to a boil. Reduce the heat to a gentle low simmer, place a lid on and cook until endives are just tender, 5 to 6 minutes. Gently transfer the endives to a plate to cool. Bring the broth to a boil again and reduce it by half, about 5 minutes. Set aside.

Use a paring knife to carefully remove the tough root ends of the endives without disconnecting the layered leaves. Season with the salt and pepper, then wrap a slice of ham around each endive half. Nestle the wrapped endives, cut side down, in the prepared baking dish.

Whisk 6 tablespoons of the heavy cream and the mustard into the reduced chicken broth and then pour into the bottom of the baking dish around the endives. Sprinkle the grated Gruyère over the endives and drizzle with the remaining 2 tablespoons heavy cream.

Place the baking dish in the oven and bake until the cheese is bubbling and golden brown in spots, about 30 minutes. Switch oven to the broiler setting until the cheese is deep golden and bubbling, 30 to 60 seconds. Serve immediately.