Roomies got a nice new blender, just got some xanthan gum in so I figured as hot as it is it's time for some alcohol freezes.
Anyone unaccustomed to xanthan gum: it's a stabilizer/thickener that will make smoothies/frapaccinos/etc not separate. Useful for artificially thickening most anything (sometimes great for fixing a dip that came out too thin). Stuffs great to have around because it only takes a tiny tiny amount for it to do it's thing, so buying it will likely last you nearly forever.
First, having the simple syrup and rum as cold as possible will help the ice not melt (meaning less ice needed and more flavor), so chill those in advance.
Two shots of rum (white preferred), the juice of about 2 limes, but maybe more (taste at the end, add more juice if not strong enough for you). A shot of simple syrup (maybe a little less). A bit less than 1/4th teaspoon of xanthan gum to stabilize, if you go too hard here it'll get weirdly thick. You can garnish with the cross section of a lime (a lime wheel) if you feel fancy.
Ice should be about two cups worth, but just add more to the blender if it's too watery at the end. If you want a mojito you can basically just add a little cut mint sprigs and blend it in very lightly.
Luckily it's all just getting smashed together so you can add more booze/lime/sugar at the end if anything seems off to you. I squeezed another lime in on the ones I made since I like it pretty sour. You can also go without xanthan gum but it will seperate with the slush on top and liquid on the bottom. There are other stabilizers out there as well
I should also note that if you're scared of the xanthan being too much just start very small and add more pinches to the blender as you go if it doesn't seem congealed enough