Place a large cast-iron skillet over medium heat with the canola oil (alternately a gas or charcoal grill can be preheated and the oil can be used to lightly grease the grates).
Divide the ground beef into 8 equal portions and shape each into a small patty about the size of your rolls. Season the outside of each patty liberally with salt and pepper and cook until seared, about 3 minutes. Turn the patties, top each with a slice of mozzarella, and continue cooking until the cheese has melted and burgers are cooked to your liking, about 3 minutes for medium.
While the burgers are cooking, place the sun-dried tomatoes into the bowl of a food processor. Pulse the machine a few times to roughly chop the tomatoes. Turn the food processor on and stream the extra-virgin olive oil in and continue mixing until the tomatoes are pureed, about 20 seconds. Reserve.
When the burgers are ready, spread each bun bottom with a hearty dollop of tomato puree. Arrange a few leaves of basil over the bun bottoms and top them with the cooked burgers. Cap each of the sliders off with the bun top and serve.
I went for sun-dried tomatoes to make the spread because of their sweet, concentrated tomato flavor -- they pack a punch and don't make your burger bun soggy.