In another large frying pan over medium-high heat, warm 1 to 2 tablespoons oil until hot but not smoking. Add the patties.
Turkey or chicken: Cook, turning frequently, until lightly browned but not yet cooked through, 4 to 5 minutes. Reduce the heat to low and continue cooking, turning frequently and brushing with all of the BBQ glaze, until the sliders are cooked through, 3 to 4 minutes.
Beef, lamb, or pork: Cook, turning frequently, until lightly browned but not yet cooked through, 2 to 4 minutes. Reduce the heat to low and continue cooking, turning frequently and brushing with all of the BBQ glaze, until the sliders are cooked to the desired doneness, 2 to 4 minutes for medium.
Plant-based Impossible Burger: Cook, turning frequently, until lightly browned but not yet cooked through, 1 to 2 minutes. Reduce the heat to low and continue cooking, turning frequently and brushing with all of the BBQ glaze, until the sliders are cooked through, 1 to 2 minutes.
Transfer the sliders to a plate. While the patties are cooking, prepare the remaining ingredients.