Batter: In a large bowl, combine flour, sugar, baking powder, baking soda, and salt. Melt 2 Tbsp of the butter. In a separate bowl, whisk together milk, egg, and the melted butter. Fold the wet ingredients into the dry ingredients, stirring just until it comes together (there should still be lumps in the batter). Set aside.
Cook Pineapple: In a large skillet set over medium heat, melt remaining 1 Tbsp butter. Add pineapple rings and cook on both sides until they begin to brown a bit, then add in brown sugar. Continue to cook until brown sugar is dissolved. Transfer pineapple rings to a plate, leaving juices in the pan.
Make Syrup: Pour coconut milk, sugar, and vanilla into the skillet with the brown sugar mixture and bring to a simmer for about 5 minutes, stirring frequently. Remove from heat and allow syrup to cool and thicken (you can pop it in the fridge to make it thicken faster).
Make Pancakes: Set a large nonstick skillet over medium/low heat. Working in batches, place a pineapple ring on the skillet then top with ¼ cup of the batter. Cook until bubbles form on top of the pancake and it begins to look dry, then flip and cook until golden brown on both sides.
Serve: Keep pancakes warm in the oven until ready to eat. Serve with a drizzle of the homemade coconut syrup. Enjoy!