Heat oven to 350 degrees F. Line a large baking sheet with parchment paper.
Make cookie dough: Cut, tear or grate paste and place in bowl with the paddle attachment of a stand mixer. Add sugar and beat, covering lip of bowl with dishtowel to get bits from flying out, until almond paste cannot be broken up any further, approximately 3 to 5 minutes at a medium-high speed. Add egg white and salt and beat until uniform and creamy.
Place sliced almonds in a wide-shallow bowl or plate. Have another bowl with water to get your hands wet.
Form cookies: Wet hands and scoop 1 tablespoon of dough into your palms. Roll it into a 4-ish inch log and drop it into the bowl of almonds. Wipe your hands dry on a towel and roll log through it. Transfer the almond-covered log to the prepared tray and arc it into a horn shape. Press any loose almonds back on. Repeat with remaining dough.
Bake cookies: For 15 minutes, or until almonds on cookies are gently toasted and horns are puffed. Let cool completely.
To finish: Melt chocolate in a small bowl and dip ends of cookies into it, then return to parchment-lined tray to set. Add sprinkles (optional).
Do ahead: Once chocolate is set, these keep in a tin for a week.
