Purée strawberries with sugar in a blender until smooth, then strain through a fine-mesh sieve into a large heavy saucepan.

Bring purée to a boil, then simmer over medium-low heat, stirring occasionally (more frequently toward end), until thick enough to mound slightly and reduced to 1 to 11/4 cups, 45 minutes to 1 hour.

Preheat oven to 200°F with rack in middle. Line a large baking sheet with nonstick liner.

Pour hot purée onto liner and spread thinly (as evenly as possible) into a 15- by 10-inch rectangle using spatula. Dry purée in oven until it feels drier (it shouldn't stick to your fingers) but is still slightly tacky, 2 to 3 hours.

Cool on liner on a rack until completely dry, at least 3 hours and up to 24.

Place a sheet of parchment paper over leather, then peel leather off liner and roll up in parchment.