Preheat the oven to 350 degrees F. Generously butter a 9-by-13-inch baking dish. Whisk together the mustard and remaining butter in a medium bowl, and then mix in the breadcrumbs, parsley, chives, 1/4 teaspoon salt and some pepper. Toss to coat and set aside.
Heat the cream and stock in a medium saucepan over medium heat. Add the celery root, bring to a simmer and cook until tender, 8 minutes.
Meanwhile, heat the olive oil in a large soup pot or Dutch oven over medium heat. Add the ham, if using, and cook until lightly browned, 5 minutes, and then stir in the shallots and cook until soft, 3 minutes. Add the Brussels sprouts, sprinkle with salt and pepper and cook until bright green and beginning to brown, 5 minutes. Add the kale and cook, stirring, until beginning to wilt, 3 minutes, and then pour in the apple cider vinegar and cook until absorbed. Remove from the heat.
Layer the bottom of the baking dish with celery root slices, and then spread the Brussels sprout mixture evenly over the top. Pour the cooking liquid from the celery root over the Brussels sprouts.
Bake until the top of the gratin begins to brown, 20 minutes. Remove from the oven and sprinkle the breadcrumb mixture over the top, and then continue baking until the breadcrumbs are toasted and the gratin is bubbling around the edges, 15 minutes. Let rest 15 minutes before serving.