Put the sweet potatoes in a large pot; cover with water and 1-1/2 tsp. of the salt. Bring to a boil, reduce the heat, and simmer until the potatoes are fork-tender, about 10 minutes. Drain and purée the potatoes in a food mill or ricer. Fold in the remaining 1 tsp. salt, the white pepper, nutmeg, cinnamon, and maple syrup. Set aside.
While the potatoes boil, cook the grits. In a medium heavy-based pot, bring the water, garlic, and shallot to a boil. Add the butter, salt, and cayenne. Gradually whisk in the grits. Bring to a boil, reduce the heat, and simmer, stirring occasionally, until the grits are cooked and creamy and just start to pull away from the side of the pot, about 30 minutes. Remove from the heat and fold in the cream.
Heat the oven to 400°F. In a large bowl, mix the sweet potato purée with the grits. Mix in the egg yolks. In a separate bowl, whisk the egg whites until they form soft peaks; gently fold them into the sweet potatoes. Spread the mixture in a 9x13-inch casserole and bake until pudding sets and the top is lightly browned, about 35 minutes.