Preheat oven to 400°F.
Combine meat with salt, pepper, grated onion, rosemary, Worcestershire, 4 cloves of garlic and a fat drizzle of olive oil. Form 6 patties thinner at center and thicker at edges for even cooking.
Trim top and bottom of tomatoes and core. Halve the tomatoes to make 2 thick cut slabs from each tomato the same thickness as your burgers.
Heat 2 tablespoons olive oil, 2 turns of the pan, in a small skillet over medium heat. Melt butter into oil, add 2 cloves chopped garlic and swirl a minute. Add panko and toss to combine, season with salt and pepper, and transfer to a bowl. When panko cools, add grated cheese, parsley and mint. Fill and mound up stuffing on the tomatoes. Bake until golden and tomatoes slumped a bit, about 12-15 minutes.
Heat a griddle or large skillet over medium high heat. Griddle burgers, 7-8 minutes turning once.
Place burgers on toast and top with stuffed tomatoes.