Preheat the oven to 350 degrees F. Peel the turnips and slice 1/8 inch thick (use a mandoline if you have one). Whisk the cream, flour, 1 teaspoon thyme, the garlic, lemon zest, nutmeg, cinnamon, 1 teaspoon salt, and pepper to taste in a large, deep skillet. Add the turnips and bring to a simmer over medium heat; cover and cook until the turnips are softened, about 3 minutes.
Stir the turnip-cream mixture and spread evenly in a 2-quart baking dish. Cover with aluminum foil and bake until the turnips are very tender, 35 to 40 minutes. Uncover and continue baking until the cream mixture is slightly thickened and the top is golden, about 10 more minutes.
Meanwhile, make the topping: Melt the butter in a large skillet over medium heat. Add the breadcrumbs, almonds and the remaining 1 teaspoon thyme and cook, stirring, until the breadcrumbs are toasted, about 4 minutes. Stir in the parsley and a pinch of salt. Remove the gratin from the oven and sprinkle with the breadcrumb topping.