Once you make granita at home, you can forget the whole homemade Popsicle game: this is way more fun. There is something really special about how flavored ice shaves off itself and breaks up into crystals and how that reacts on your tongue. Just like a kiss.
Combine the condensed milk, water, coconut milk, cardamom, coffee, sesame seeds, lime juice, and zest in a big bowl and give it a good whisk. Run the mixture through a sorbet machine or freeze it in a pan, running a fork through it every 30 minutes until frozen.
Scoop and serve the shaved ice in a bowl with the lychees, the mint, and a little more condensed milk drizzled over top.