Mince the onion and place it in a microwave-safe container. Cover loosely with plastic wrap and microwave at 600W for 1 minute. Let it cool.

In a bowl, combine breadcrumbs and milk. Let it soak, then add ground meat, minced onion, salt, and pepper. Mix until sticky. Divide into two portions and shape into oval patties.

Heat vegetable oil in a frying pan over medium heat. Cook the patties until browned on one side, then flip and brown the other side. Cover with a lid and cook on low heat for about 6 minutes. Place a slice of cheese on each patty, cover, and heat for 1 minute until melted. Remove and plate.