Chill the pineapple juice and coconut cream thoroughly to minimize melt and keep the drink thick; if the coconut cream is very solid, stir it briefly just to loosen before measuring.
Add the pineapple juice and coconut cream to the blender first so the frozen fruit doesn’t jam the blades and the mixture emulsifies smoothly from the start.
Add the frozen pineapple chunks and blend on high until the mixture is thick, smooth, and fully uniform.
Add the lime zest and blend for 2–3 seconds only, just to distribute; over-blending zest pushes bitterness and kills aroma.
Check the texture and adjust as needed: if too thin, add ice in small handfuls and blend briefly until slushy; if too thick to pour, add 1–2 tablespoons pineapple juice and pulse.
Pour into glasses and serve right away; the drink should be smooth, creamy, very cold, and spoonable-slushy in texture.