Place one medium and one large skillet over medium-high heat with 2 turns of EVOO in each pan, about 2 tablespoons each. When the oil is hot, place the sliders into the large pan (as many as will fit comfortably, don’t crowd the party!). Cook until golden brown on the outside and cooked through inside, 3-4 minutes per side. Removed the cooked sliders from the pan to a dinner plate and cover them with foil to keep warm while the others cook.
While the sliders are cooking up in the large pan, place the sliced shallots into the other pan and cook until softened and caramelized, 8-10 minutes. Season the shallots with salt and freshly ground black pepper, then remove the pan from the heat and add in the sherry. Return the pan to the heat and cook away the liquid, scraping the bottom of the pan with a wooden spoon or spatula to free up all those tasty bits that are stuck to the bottom.
While the burgers and shallots are cooking, split the buns in half and place them onto a baking sheet. Toss them into the oven or under the broiler for a few minutes to toast them up.
Assemble the sliders by placing a patty down on each bun and topping them off with a hearty scoop of caramelized shallots. Serve each person four sliders each and enjoy the show!