1 small pineapple, trimmed and cut into 1-inch chunks
1 (13.5-ounce) can unsweetened coconut milk
1 (15-ounce) can cream of coconut
3 limes, divided
¼ teaspoon kosher salt, divided
½ cup white rum, divided
½ cup agave syrup
Directions
Transfer pineapple to a freezer-safe zip-top bag or airtight container and freeze at least 4 hours or until firm.
In a food processor, process coconut milk, cream of coconut, the juice of 1 ½ of the limes, ⅛ teaspoon of the salt, and ¼ cup of the rum until frothy, about 2 to 3 minutes.
Transfer to a small bowl and refrigerate until ready to use.
In the same food processor bowl (no need to clean between uses), process frozen pineapple, the zest of 1 lime, juice of the remaining 1 ½ limes, remaining ⅛ teaspoon salt, and agave syrup until only small chunks remain visible.
Add remaining ¼ cup rum and process until mostly smooth.
Spread ⅓ of the pineapple mixture into the bottom of a standard loaf pan or freezer-safe container with a lid.
Top with ⅓ of the coconut mixture.
Repeat with remaining pineapple and coconut mixtures until all are used.
Freeze, covered, at least 4 hours or overnight. If using a loaf pan, cover with plastic wrap.
Serve sorbet and top with toasted coconut flakes, if desired. Store any leftovers in a lidded freezer-safe container.