Dice honeydew melon, discarding rinds. Place on a wax paper lined baking sheet and freeze until frozen. If not using right away, place frozen cubes into a large ziplock bag and keep in the freezer.
Combine tequila and jalapeno slices in a glass jar or bowl, and let stand 2-4 hours. Strain solids and discard, keeping the infused tequila.
To a small plate, add corn syrup. To another small plate, add sugar, salt and lime zest, using a fork to combine. Dip rims of serving glasses in corn syrup, then in the sugar/salt mixture. Set aside.
Add frozen honeydew cubes, ice cubes, water, honey, lime juice, and infused tequila to a large blender. Blend until smooth, about a minute or so.
Pour into serving glasses and enjoy!