Pat pork tenderloins dry with paper towels. Rub with 1 tablespoon olive oil, salt, pepper, garlic, and smoked paprika.
Heat the remaining 2 tablespoons of olive oil in a large oven-proof skillet over medium-high heat.
Sear the pork on all sides until golden brown, about 6–8 minutes.
In a small saucepan, combine Pineapple Aji Amarillo Jam, tamari, and lime juice. Heat over low until smooth and slightly thickened, 3–4 minutes. Brush half of the glaze over the seared tenderloin. Transfer skillet to the oven and roast for 10 - 15 minutes, or until pork reaches an internal temperature of 145°F.
Remove pork from oven and brush with remaining glaze. Rest for 5 minutes before slicing.
Garnish with fresh cilantro or parsley, if desired.