Heat olive oil in a large skillet over medium heat. Add Swiss chard; cook and stir until wilted, about 5 minutes. Transfer chard to a colander and let cool, about 5 minutes. Press out as much moisture as possible.
Mix chard, bread crumbs, Parmesan cheese, salt, and black pepper together in a bowl. Stir in beaten egg until combined. Shape into 1/2-inch thick patties.
Heat canola oil in a large skillet over medium heat. Cook patties in hot oil until browned, about 3 minutes per side.