Boil the sweet potatoes in their skins until tender. Peel and mash until smooth.
In a bowl, combine the mashed sweet potato, egg, breadcrumbs, crumbled feta cheese, crushed garlic, salt, and pepper.
Shape the mixture into patties. Heat olive oil in a skillet over medium heat and cook the patties until golden brown on both sides.
Toast the inside of the burger buns until lightly golden.
Slice the tomatoes thinly and prepare the arugula.
Assemble the burgers: Place arugula on the bottom bun, top with a sweet potato patty, and then layer with tomato slices. Cover with the top bun.
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