Preheat the oven to 375 degrees F. Melt the butter in a small skillet over medium heat. Add the breadcrumbs and gingersnap crumbs and cook, stirring, until lightly toasted, 3 to 5 minutes; set aside.
Combine the heavy cream, maple syrup, thyme, allspice, 1 1/2 teaspoons salt and the cayenne in a medium saucepan. Bring to a boil, then remove from the heat.
Butter a 3-quart baking dish. Spread a single layer of sweet potatoes in the bottom of the baking dish and pour about one-third of the cream mixture on top. Repeat to make 2 more layers of potatoes and cream. Cover with foil and bake 40 minutes. Uncover and continue to bake until the cream is bubbling and the potatoes are lightly browned and tender when pierced with a knife, 40 to 50 more minutes, sprinkling the breadcrumb mixture over the potatoes during the last 5 minutes of baking.