Mix first eight ingredients in a large bowl. Form into patties or sliders. Mix thoroughly but avoid over-handling / over-compacting meat.
Let patties rest thirty minutes at room temperature before grilling.
Prepare medium-hot fire charcoal grill. When grill is ready, brush rack with vegetable oil so that meat doesn't stick. Place patties on rack, cover, cook, turn only once until done to preference, approximately 5 minutes each side (depending on size). Immediately before removing from grill, top with cheese.
Let burgers rest for five minutes.
Brush sourdough with olive oil; grill lightly.
Spread basil pesto on bread. Add toppings of your choice such as tomatoes, red onion slices, arugula, etc.
Enjoy!