Place the fresh chopped pineapple in a blender. If using frozen pineapple, allow it to partially defrost before blending. Add brown sugar, lime juice, and vanilla extract. Add coconut milk.
Blend on medium until smooth. Use the pulse feature to minimize the foaming, which will reduce the chance you'll have air bubbles in the pineapple popsicles. Tap the blender container on the counter a few times to release air bubbles.
Pour the mixture into popsicle molds, stopping at about a quarter inch from the top as the popsicles will expand a bit while freezing.
Snap on the lids for your molds. The sticks should protrude about an inch.
Freeze the popsicles for a minimum of 6 hours.
Remove the popsicles from the molds. If using plastic mold, it helps to dip the mold in hot water for about 10 seconds before trying to release the popsicles.
Store the popsicles frozen in bags or wrapped in plastic. They will be good for about one month. They don't necessarily go bad, but the flavors won't taste as good after that time.