Preheat oven to 350°. Spread almonds on a baking sheet and toast in oven until browned and fragrant, about 8 minutes.
Meanwhile, heat milk in a saucepan over high heat until hot. Stir in hot almonds and 1/3 cup sugar; let cool. Chill, covered, at least 8 hours or overnight.
Pour almond-infused milk through a strainer into a metal loaf pan; discard nuts.
In another metal loaf pan, stir coffee and remaining 1/3 cup sugar until sugar dissolves. Wrap both pans airtight; freeze. After 2 hours, stir slushy liquid with a fork, scraping sides of pans to create larger granita flakes. Return pans to freezer until completely frozen, about 4 hours.
Chill 8 bowls. Remove pans from freezer 5 to 10 minutes before you want to serve granita. Using a fork, scrape tops of granita to break into flakes. Spoon about 1/2 cup coffee granita into each chilled bowl and 1/2 cup almond milk granita alongside.
Make ahead: Up to 4 days.
Note: Nutritional analysis is per serving.