Peel sweet potatoes and cut into 1/4-in. slices. Butter an 8- by 8-in. pan and arrange slices in layers, sprinkling with salt, pepper, and thyme as you go. Cover with aluminum foil and bake potatoes until they are tender when pierced with a fork, 45 to 90 minutes.
Over high heat, bring 1 cup water to a boil in a medium pot. Reduce heat to maintain a simmer. Put egg whites and cream of tartar in a rimmed metal bowl just big enough to fit into pot over water. Set bowl over pot and whisk egg whites constantly until hot but not cooking, 3 to 5 minutes. Take off heat and beat until firm peaks form.
Sprinkle in sugar and vanilla and beat into stiff, shiny peaks.
Spread over cooked sweet potatoes. Put under a broiler until nicely browned and serve hot.
