Grate the onion using the large holes of a box grater; add the grated pulp but leave any excess liquid behind.
For a vegan option, replace the egg with a flax egg (combine 1 tablespoon ground flaxseed with 2.5 tablespoons warm water and let thicken for 5 minutes). Vegan patties may require slightly longer cooking to firm up.
For a gluten-free alternative, consider using a quinoa burger recipe instead.