Step 1

Bring strawberries and 2 cups water to a simmer in a large saucepan over medium-high heat. Reduce heat, cover partially, and simmer gently, swirling occasionally, until strawberries are softened and have lost most of their color, 15–20 minutes.

Step 2

Strain into a small saucepan, pressing on berries to extract as much liquid as possible; reserve berries for another use. (You should have about 1 cup liquid.) Add sugar to liquid in saucepan and return to a simmer. Remove from heat and stir until sugar is dissolved. Let cool, then cover and chill until cold, at least 1 hour.Do ahead: Syrup can be made 2 weeks ahead. Keep chilled.

Step 3

To make 1 cocktail, combine rum, Cappelletti, lime juice, ½ oz. strawberry syrup, and a small pinch of salt in a cocktail shaker. Add 4–6 ice cubes, cover, and shake vigorously until outside of shaker is very cold, about 20 seconds. Double-strain into a coupe glass. Garnish with a strawberry.