Melt the butter in a pan, add the onions, cover and sweat until soft. Allow to cool and then mix in a bowl with all the other ingredients.
Shape into burgers and toss in seasoned flour, patting off excess. Fry in the olive oil over medium heat, turning as required until fully cooked (internal temperature of at least 160°F) about 4 minutes each side.
Serve on a toasted bun with cheese shavings, lettuce, onion slice and a dollop of Guinness Irish Ketchup .