Add eggs, lime juice, and honey to a large bowl
Mix on high speed for 5 minutes
Add coconut milk to a medium saucepan
Heat milk over medium-low heat until it just starts to warm up
While whisking egges, slowly add the conconut milk about one tablespoon at a time until it is all combined
Pour mixture back into the saucepan and return to heat
Stir for 10 to 15 minutes until mixture thickens
Remove from heat
Pour into ramekins and/or a popsicle mold
Allow to cool to room temperature
Refrigerate pudding. Place popsicle mold in freezer
Chill or freeze for several hours