Mince the onion. Slice the carrot into rounds and cut star shapes. Mince the leftover carrot pieces.

Cut broccoli into small florets. Shape the melting cheese into stars using a cutter.

Place minced onion and carrot in a microwave-safe container, cover loosely with plastic wrap, and microwave at 600W for 1 minute. Let cool.

Place carrot stars and broccoli florets in another microwave-safe container, cover loosely, and microwave at 600W for 3 minutes.

Mix breadcrumbs and milk in a bowl and let soak.

Combine the ground meat, cooled vegetables, beaten egg, soaked breadcrumbs, and salt and pepper in a bowl. Mix well and divide into two portions. Shape into oval patties with a slight indentation in the center.

Heat salad oil in a frying pan over medium heat. Add the patties and cook until browned. Flip, cover, and cook on low heat for 7–8 minutes. Place cheese stars on top, turn off the heat, and cover until cheese melts.

Add ketchup and Worcestershire sauce to the pan and simmer over medium heat to create the sauce.