Pierce the sweet potato multiple times on all sides with a fork, then place on a microwave-safe plate and lightly tent with a damp paper towel. Microwave on high for 4 minutes, rotate, and continue to cook in 2-minute increments until it is soft, 8 to 10 minutes total. The exact cooking time will depend on your microwave’s wattage. Let cool, then peel the sweet potato, place the flesh in a bowl, and use a fork to mash it.
In a small saucepan or skillet over medium-low heat, warm the olive oil. Add the onions and sauté until softened, about 4 minutes. Add the garlic and Italian seasoning and continue to sauté until the onions are translucent, 2 to 3 minutes more.
Add the onion mixture to the bowl with the mashed sweet potato and mix in 1/4 cup of the bread crumbs and the cheese. Season with the salt and pepper, mix to combine.
Using an ice cream scoop, scoop a ball of the mixture, then use your hands to press it into a patty, about 1/2 inch (12 mm) thick and 3 inches (8 cm) in diameter. Repeat with the remaining mixture to make 6 patties.
Set up a breading station, putting the flour, egg, and remaining 3/4 cup of bread crumbs in three separate shallow bowls. Lightly dredge the patties in the flour, dip into the egg, and then into the bread crumbs.
Heat 1/4 inch (6 mm) of olive oil in a large nonstick skillet over medium heat. Fry the sweet potato patties until golden brown, 3 to 5 minutes per side. Transfer to a paper towel-lined plate to drain.
Serve with a dollop of crème fraîche or sour cream and a sprinkling of chives.