Begin by seasoning the pork with salt, pepper, and pimenton, mixing well by hand to combine.
Form into two-inch patties for sliders, four inch patties for full size burgers, and brush both sides with olive oil. Scatter onions on a sheet pan or cutting board, press sliders onto onions, turn and repeat on other side.
For Bacon Jam: cook the bacon over medium to medium-low heat, adjusting the heat as necessary and stirring often, until browned and crisp and the fat is rendered. Drain the bacon on a paper-towel lined plate. Reserve a few tablespoons of drippings in the skillet.
Add the shallots to the reserved drippings and cook over medium low heat about 2 minutes, stirring often and scraping up the browned bits. Return the bacon to the pan; add the red pepper flakes, brown sugar, vinegar, orange juice, rum, ginger, and honey. Bring to a boil, then reduce the heat and simmer, uncovered, about 10 to 15 minutes or until most of the liquid is evaporated, stirring occasionally.
Transfer to a mini-food processor; pulse until the bacon is finely diced but not pureed, turning off the motor several times to scrape down the sides of the bowl. Remove from food processor and set aside.
Place a skillet or griddle on the barbecue grate over medium high heat. It is hot enough when a drop of water bounces and sizzles. Place the burgers on the skillet or griddle. Press down on each burger with a spatula. Turn after 3 minutes (4 for the larger burger) and cook for another 3-4 minutes until medium to medium rare. Remove from grill, place on buns, top with a dollop of Bacon Jam, and serve.