Melt the butter in a large saucepan over medium-high heat. Add the onion and cook until softened and light golden brown, about 6 minutes. Add the ham and cook, 2 minutes. Add the cream, milk, cheese, 1/4 teaspoon salt, and 1/4 teaspoon pepper and bring to a boil. Reduce heat to medium-low. Simmer until thickened, about 4 minutes. Add the cauliflower. Transfer to a 2-quart casserole dish and sprinkle with the bread crumbs and thyme. Cover with aluminum foil. Bake for 20 minutes. Uncover and continue baking until the cauliflower is tender, 15 to 20 minutes. Remove from oven and let rest at least 5 minutes before serving.
Tip: Make this a vegetarian side dish by skipping the ham.