In a small pot with tight fitting lid heat EVOO, a couple of turns of the pot, over medium heat, add garlic and stir 2 minutes then add tomatoes and cover pot, raise heat a bit and cook tomatoes, shaking the pot occasionally, until tomatoes burst, 8-10 minutes. Mash up sauce with wooden spoon and season tomatoes with salt and pepper. Thicken, uncovered for 2-3 minutes, then stir in basil leaves and turn off heat.
Meanwhile, season chicken with thyme, salt and pepper or veal with sage, salt and pepper. In a separate dish, combine breadcrumbs with sesame seeds and parm cheese, parsley. Form 8 small patties 3 inches wide and coat in breadcrumbs, gently pressing patties into crumbs to make them stick. Heat a drizzle of oil in a large, shallow non-stick skillet or on a non-stick griddle plan over medium to medium-high heat. Cook patties to golden brown and cooked through, about 3 minutes on each side.
Place a spoonful of soft burata or ricotta on bun bottom. Drizzle cheese with a touch of EVOO and season with salt and pepper. Top soft cheese with a few leaves of arugula, then the patties, then some sauce and bun tops.