Preheat the oven to 400°F.
Cut enough of the pineapple into ½" cubes to equal 2 cups. Cut remaining pineapple into rings and set aside.
In a blender, combine pineapple cubes, brown sugar, lemon juice, paprika, ginger, and garlic. Blend until smooth and transfer to a medium saucepan. Bring mixture to a simmer over medium-high heat, and simmer for 5 minutes.
Heat oil in a large, heavy ovenproof skillet (such as cast-iron) over medium-high heat. Season pork roast with salt. When oil simmers, add the roast and brown, turning occasionally, until browned all over.
Lightly brush roast with pineapple glaze and transfer skillet to the oven. Bake, brushing the roast with more glaze every 15 minutes, until the internal temperature reaches 145°F, about 45 minutes.
After pork has been in the oven for 25 minutes, place pineapple rings on a lightly oiled baking sheet and brush with glaze. Roast until browned, about 20 minutes.
When roast is done, transfer to a cutting board and let rest 15 minutes before slicing.
Slice and serve pork with the roasted pineapple slices.