Prepare the berries. Wash, hull, and divide the strawberries in two groups. Slice one group of the berries and set them aside for later. Add the remaining group of whole berries to a blender or food processor and blend until completely smooth.

Simmer the base. Transfer the strawberry purée to a saucepan. Whisk in the cornstarch, 3 tablespoons of sugar, and the lemon juice until the mixture is evenly combined. Set the pan over medium-high heat and cook, stirring now and then, until the sauce comes up to a boil. Let it boil briefly so the cornstarch can fully thicken the mixture.

Add the fresh berries. Remove the pan from the heat and stir in the sliced strawberries. Give the sauce a taste and adjust the flavor as you like — add extra sugar for sweetness or a bit more lemon juice for brightness. If the sauce is thicker than you prefer, thin it out with a teaspoon of water at a time.

Cool and serve. Allow the sauce to cool (it will continue to thicken as it stands), then spoon over cheesecake or refrigerate in a sealed container until ready to use.