Preheat the broiler.
Melt the butter over medium heat in a large skillet. If you do not have a skillet large enough to place four burger patties flat on the bottom, then aim to cook the patties in batches.
Place the patties flat on the bottom of the skillet. Cook for 3 minutes, or until browned, then flip and repeat.
Meanwhile, toast the burger buns under the broiler.
When the buns are golden, spread them with a thin layer of aioli.
When the patties are cooked through and richly browned, layer them inside the burger buns with the remaining toppings, including a large fistful of spinach.
Serve with napkins (these guys get messy!).