Put the almonds, sugar, almond extract, and cinnamon in a food processor and pulse until very finely ground, about 5 minutes, stopping to scrape down the bowl every minute or so.
Slowly pour 1⁄4 cup hot water in through the lid and process until the mixture is a fine paste.
Add another cup hot water in the same way. The mixture will lighten in color slightly and become a concentrated almond “milk.”
Transfer the mixture to a 9-by-13-inch glass baking pan. Add cold water and stir to combine. Cover with aluminum foil and put in the freezer for 1 hour.
After 1 hour, uncover the pan and scrape the edges of the granita with a fork, stirring the ice pieces into the center, then cover again and return to the freezer until solid, scraping and stirring every 30 to 45 minutes. When the granita is frozen solid, scrape the surface with a fork and scoop it into serv- ing glasses. Serve immediately.
How to store: The granita will keep in the freezer in an airtight container for up to 4 days.