Shape the mixture into 4 patties, using about 3/4 cup for each. Heat a large cast-iron or nonstick skillet over medium-high heat. Add oil; when it is shimmering, add the patties. Cook, flipping once or twice, until very browned and crisp, 5 to 8 minutes total. Transfer to a rack and let cool for 5 to 10 minutes. Serve the burgers on buns.