How to Make It
In a medium bowl, combine the grated sweet potatoes and onion. Squeeze dry in a clean kitchen towel, then stir in the egg, flour and thyme; season with salt and pepper.
In a large skillet, heat 2 tablespoons of the olive oil. Spoon eight 1/4-cup mounds of the sweet potato mixture into the oil and pat them into 1/2-inch-thick rounds. Cook over moderately high heat, turning once, until golden, about 4 minutes per side. Transfer the sweet potato cakes to a platter and keep warm.
Wipe out the skillet and heat the remaining 1 tablespoon of olive oil. Add the garlic and cook over moderate heat until softened but not browned, about 1 minute. Add the corn and cook, stirring, until some of the kernels are browned, about 3 minutes. Spoon the corn over the sweet potato cakes, sprinkle with the goat cheese and basil and serve with lemon wedges.