Start the rice: Rinse 1 cup jasmine rice until the water runs clear. In a saucepan, combine rice, 1 can coconut milk, and 1/2 cup water.
Add a pinch of salt. Bring to a gentle simmer, stir once, cover, and reduce heat to low. Cook 12–15 minutes, then rest off heat for 5 minutes.
Prep the pork: Pat pork dry.
Slice pork tenderloin into 1/2-inch medallions, or pound chops to an even 1/2-inch thickness. Season both sides with salt and pepper.
Make the sauce mix: In a bowl, combine 2 tablespoons soy sauce, 1 to 2 tablespoons honey, zest of 1 lime, juice of 1 lime, 1 tablespoon finely grated ginger, 2 minced garlic cloves, and a pinch of red pepper flakes.
Sear the pork: Heat 1 to 2 tablespoons oil in a large skillet over medium-high. Add pork in a single layer and cook 2–3 minutes per side until browned and just cooked through.
Transfer to a plate and tent loosely with foil.
Build the pan sauce: Lower heat to medium. Add a drizzle more oil if needed, then add remaining grated ginger and 1 minced garlic clove. Cook 20–30 seconds until fragrant.
Pour in the sauce mix and simmer 1–2 minutes until glossy and slightly thickened.
Coat and finish: Return pork and any juices to the skillet. Toss to coat and warm through, 1 minute. Squeeze in more lime if you like extra tang.
Adjust salt, soy, or honey to taste.
Fluff and serve: Fluff coconut rice with a fork. Plate rice, top with ginger lime pork, spoon over extra sauce, and finish with chopped cilantro or scallions.