Combine sweet potatoes and 2 tablespoons butter in a large bowl, tossing to coat. Combine flour and next 3 ingredients; sprinkle over potatoes and toss to coat.
Place remaining 2 tablespoons butter in a 10" cast-iron skillet or other large ovenproof skillet. In the skillet, arrange sweet potatoes in a single layer, in slightly overlapping circles. Top with remaining sweet potatoes.
Cut a circle of non-stick aluminum foil; place over potatoes. Place a 9" cast-iron skillet on top of foil to weigh the galette. Cook over medium heat for 5 minutes; don't remove cover. Transfer weighted skillet to oven; bake at 375° for 10 minutes. Remove top skillet and foil; and bake 15 more minutes, or until potatoes are tender. Loosen edges with a spatula and invert onto a serving plate.