Mix all ingredients, except the oil and buns, in a large bowl. Divide mixture into 4 equal portions and shape into burgers.
Meanwhile, heat a stovetop grill pan (or skillet over high heat) until it’s very hot.
Brush tops of the burgers with some of the oil. Place the oiled side down on the grill pan and cook for 3-5 minutes. Before turning, brush the unoiled tops with the rest of the oil; turn and cook an additional 3-5 minutes This will produce a rare to medium-rare burger. Cook a bit longer for medium or well but lower the heat.
Remove the burgers to a platter and tent with foil to keep warm. Keep the grill pan over the heat for the buns.
Split the brioche buns and place the cut sides down on the grill to toast.
Serve burgers on the toasted rolls. You may like to layer some lettuce and tomato on the bun under the burger, as shown in the photos.