Preheat the oven to 325 degrees . Place a cooling rack on a baking sheet. Using a 3-inch cookie cutter or an empty 4-ounce can, cut 16 bread rounds from the bread slices and arrange on the baking sheet. Toast until light golden, 7 to 8 minutes. (Reserve the crusts in the freezer for another use, like breadcrumbs or stuffing.)
Season the pork with the onion, paprika, garlic, a little salt and lots of black pepper. Place the pastrami in the food processor bowl and pulse into a very fine chop. Add the pastrami to the pork, mix and form into eight 3-inch patties. In a nonstick skillet or griddle, heat a drizzle of EVOO over medium-high heat. Add the patties and cook until cooked through, 3 to 4 minutes on each side.
Place each burger on a bread round and top with a slice of pickled tomato. Slather lots of mustard on the remaining bread rounds and set in place on top of the tomatoes. Arrange the pickles on top of the bread and secure them with toothpicks.