In a large skillet, over medium low heat, heat the olive oil and sauté the onions, stirring occasionally, until they start browning. Add the beer and the brown sugar and cook until thickened and reduced by less than half, about 20 minutes. Reserve.
Vegan Olive Tapenade:
Process the ingredients in a food processor until the desired consistency. I like mine smooth. Reserve.
Sliders:
Preheat oven to 350F degrees.
Assemble patties on a baking sheet sprayed with non stick cooking spray and bake them for 15 minutes, flipping them over halfway, until they are crispy.
During the last 3 minutes of cooking time, add the buns to the oven to toast.
Take the patties and buns out of the oven.
Turn the broil on, top the patties with the provolone cheese (if using) and pop them back in the oven until the cheese melts, about 2 minutes.
Lightly brush the bottom buns with mayo (if using) and then top with lettuce, the patties, a little olive tapenade and the caramelized onions.