2medium onions, peeled, sliced and separated into rounds
Prepare the caramelized onions first. Heat the butter and olive oil in a large pan over medium-low heat. Add the onions, cover the pan and cook for 12 to 15 minutes, stirring 3 or 4 times during the process.
Remove the cover, raise the heat to medium and add the salt. Continue cooking, uncovered, for 15 minutes, stirring frequently and loosening any browned bits that may accumulate on the bottom of the pan.
Add the water and continue cooking until the liquid has evaporated and the onions are nicely caramelized, about 8 to 10 minutes longer. Transfer to a bowl and set aside.
While the onions cook, trim the pork tenderloins of any silver skin or excess fat. Slice into 1/2-inch thick pieces and season on both sides with salt and pepper.
Combine the maple syrup and mustard in a small bowl. Combine 1-1/2 tablespoons of the mixture with the caramelized onions and set the remainder aside.
Coat the bottom of a large pan with vegetable oil and heat over medium-high heat. Add half the pork slices in a single layer and sear until lightly browned, about 1-1/2 minutes per side.
Transfer to a plate, add a little more oil if necessary and repeat with the remaining pork. Transfer to the plate with the first batch of pork, wipe out the pan, reduce the heat to medium and add the butter.
Add the maple syrup-mustard mixture to the pan and heat until bubbly. Return the pork to the pan and, using a pair of tongs, turn the slices to coat with the sauce.
Add a few grinds of black pepper if desired and remove from the heat. The recipe can be made ahead to this point.
To serve, place one slice of pork on each bun, top with some onions and secure with a pick.
Tips for Making This Recipe
If you decide to make the pork and caramelized onions ahead of time, reheat on medium (50%) power in the microwave. Cook just long enough to take the chill off and warm slightly. You don't want to overcook or dry out the pork.