1Preheat oven to 375F. For the garlic spread, place the cut garlic, olive oil, salt, and pepper into a roasting pan with a lid, or wrap garlic heads in foil and place directly on oven rack. Roast in oven for 40-45-minutes or until garlic is soft and golden. Once cooked, squeeze the softened garlic out of its skin and into a bowl. Add the olive oil from the roasting pan to the bowl and mash together until smooth and creamy. Season with salt and pepper and set aside.
2To prepare the burgers, combine all the spice mix ingredients into a small bowl and mix well. In a larger bowl or on a plate, add ground lamb and season with spice mix, making sure spices are well incorporated. Portion into patties and let them rest at room temperature for 15 minutes to allow flavors to meld.
3Heat grill to high, then grill burgers to desired temperature. While the meat is cooking, add onion, jalapeno, mint, and arugula into a mixing bowl and toss with a drizzle of Trefethen olive oil, seasoning with salt and pepper to taste. Lightly oil each half of the brioche buns and grill briefly to warm the bread.
4To assemble, lay the bottom buns onto your favorite plate and cover generously with the garlic spread. Place cooked meat and arugula mixture on top of bread and top with other half of bun. Enjoy!