Finely chop the dill, spring onions, and capers, and add it all to a small bowl with the mayonnaise, mustard, salt, pepper, and sugar. This will be your burger dressing.
Set up the breading station for the halloumi: flour, beaten egg, and breadcrumbs. Add a pinch of seasoning (salt and pepper) to each.
Cut the halloumi lengthwise in two (so that you have 2 halloumi burger patties.
Roll each halloumi patty through the flour, then the beaten egg, and finally the breadcrumbs.
Set a pan over medium-high heat and add 1 cup of oil to it.
When the oil is hot, add the halloumi and fry on one side until golden, and then flip and cook on the other side until golden. It will be about 2 minutes per side.
Remove the halloumi to a wire rack or plate with paper towels on it to absorb the oil.
(Optional) – Toast the burgers (face down) in a dry pan over medium heat (about a minute or so). You don’t need any butter or oil if using brioche buns.
Assemble the burgers: toasted bun, halloumi patty, a couple tablespoons of the burger dressing, a thick slice of tomato, and a couple of leaves of lettuce.