Cut each pork tenderloin, widthwise, into 4 equal pieces. Place a piece of the pork on a cutting board and cover with plastic wrap. Gently pound or firmly press each piece of pork into a medallion about 3/4" thick. Repeat with remaining pork. Plate and refrigerate until needed.
Preheat the oven 375 degrees F. Set pineapple on parchment paper-lined baking sheet. Spread 1 tsp. of butter on each pineapple round. Bake 25 to 30 minutes, or until the pineapple is tender.
While the pineapple cooks, heat the oil in a skillet set over medium-high. Season the pork with salt and pepper and cook 3 minutes on each side, or until just cooked through. Transfer pork to a clean plate.
Place the remaining ingredients, except lime slices, in a bowl and whisk to combine. Pour the mixture into the skillet, bring to a simmer, and simmer two minutes, until thickened. Return pork to the skillet and heat through 2 to 3 minutes.
To serve, set a piece of pineapple on each of 4 plates. Set 2 pieces of pork tenderloin on each slice of pineapple and spoon over the sauce. Garnish with lime slices, if desired, and serve.