Using a French press will create a strong coffee that keeps its bold flavor even when frozen.
Place a 13- x 9-inch baking pan in the freezer. Place coffee in a French press and add the boiling water. If using a drip coffee maker, substitute the same amount of cold water and brew.
Combine the sugar, cinnamon, mint, and ginger in a medium bowl. While the coffee is still hot, pour it over the sugar mixture in the bowl, stirring well until the sugar is dissolved. Let steep for flavors to combine (about 30 minutes). Strain 1/2 of the coffee into the cold baking pan and 1/2 into a pitcher. Return the baking pan to the freezer and put the pitcher in the refrigerator.
Check the pan in the freezer after about 2 hours. Using a large fork, scrape any frozen coffee around in the pan; continue to check and scrape the pan every hour for an additional 2 hours. (Once it is made, the granita may be used as needed for up to one week; keep covered with plastic wrap.)
To serve: Fill a medium glass 1/2 full with frozen coffee granita. Drizzle 1 teaspoon sweetened condensed milk over the granita. Fill the glass with the cold refrigerated coffee. Top with milk as desired; serve.