Combine beef with finely chopped onion and Vegeta marinade, mix to blend and allow to rest for about 30 minutes. Form 4 burgers the size of the buns.
Cut each bun in half and toast them in an ungreased large-size frying pan, cut side down. Remove, wipe the frying pan with a paper towel, add bacon strips and fry until golden brown.
Add 2 tablespoons of oil and when the oil is hot, fry the burgers on both sides until done. Remove the burgers, add the remaining oil and fry the eggs sunny side up.
Spread mayonnaise or mild relish on the bottom half of the bun. Add fried bacon, burger, a slice of cheese and top with fried egg.
Close with the top part of the bun and serve immediately.
When you make burgers, be careful not to knead the mince too much. Combine the ingredients and quickly shape into thick patties. They will dry out if too thin. If you prefer mixed mince burgers, you can add up to ¼ ground pork to the beef.