Preheat oven to 375 degrees. Butter four 3/4-cup ramekins; set aside. In a medium saucepan, melt butter over medium-low heat. Add onion, garlic, and thyme; season with salt and pepper. Cook, stirring often, until onion is softened, about 8 minutes. Stir in flour; cook, stirring, 3 minutes.
Gradually whisk in milk; simmer, whisking constantly, until thickened, about 2 minutes. Remove from heat, and stir in 1/2 cup cheese and 1/2 teaspoon salt. Whisk in sweet-potato puree, then egg yolks, one at a time.
In a clean mixing bowl, beat egg whites with a pinch of salt until stiff peaks form. Whisk 1/4 of whites into cheese mixture. Using a rubber spatula, gently fold in the rest.
Place ramekins on a rimmed baking sheet. Pour mixture into ramekins; sprinkle with remaining cheese. Bake until puffed and golden brown, 15 to 20 minutes.