Preheat oven to 350°F (180°C). Line a rimmed baking sheet with parchment paper.

On prepared pan, toss together strawberries and sugar until combined; spread in a single layer.

Bake, stirring every 5 to 10 minutes, until berries are very soft and fragrant and juices are deep red and starting to thicken at edges of pan, 20 to 25 minutes. Let cool completely on pan.

Using a fine-mesh sieve, thoroughly strain strawberries. Reserve any juice for another use. (See Note.)

Place strained strawberries in the work bowl of a food processor; process until puréed, stopping to scrape sides of bowl.