Preheat a gas grill or grill pan to medium high heat.
To make the artichioke aioli, puree the artichoke hearts, mayonnaise, garlic, and cheese together in a mini food processor.
To make the patties, combine the ground beef, grated onion, garlic, salt and pepper in a large bowl. Be careful not to overwork the meat. Form the meat into 6 equal patties making a slight indentation in the center of each one.
Brush the grill pan with oil. If using a grill pan, toss the grape tomatoes on the grill and cook, turning them occasionally until charred and slightly softened. If using a traditional grill, heat 1 tablespoon of oil in a large skillet and cook the tomatoes in the skillet on the grill. Season the tomatoes with salt to taste and set them aside in a bowl.
Cook the burger patties on the grill, about 4 minutes each side. Place the slices of burrata on the patties during the last 2 minutes of grilling so that it melts slightly.
Lightly toast the pieces of focaccia on the grill. To assemble the burgers, place some baby arugula on each focaccia bottom and top with a burger patty. Place 2 pieces of crispy pancetta on each patty and top with some charred tomatoes. Spread some artichoke aioli on the cut side of each focaccia top. Add the tops and serve.