Do ahead: Sauce can be made up to 3 days ahead. Cover and chill. Rewarm slightly before serving.
- 2 16-oz bags frozen blackberries
- 1 cup sugar
- 2 Tbsp fresh lemon juice, divided
- 4 tsp cornstarch
- 1/2 tsp finely grated lemon peel
Bring frozen berries and sugar to simmer in heavy large saucepan over medium-high heat, stirring often. Simmer 1 minute. Stir 1 tablespoon lemon juice and cornstarch in small bowl until cornstarch dissolves. Add to berries and stir until thickened, about 1 minute. Mix in remaining 1 tablespoon lemon juice and lemon peel. Cool slightly. Serve warm or at room temperature.