Rinse the pork loin thoroughly under cold water, pat dry with paper towels, and lightly trim any excess fat.

In a small bowl, mix the smoked paprika powder, fine table salt, and ground black pepper with the olive oil. Rub the pork loin evenly all over with this spice mix.

For the glaze, whisk the barbecue sauce with maple syrup, medium-hot mustard, apple cider vinegar, and the finely chopped garlic cloves in a bowl until smooth. Set aside one third of the glaze for brushing later.