1 lb strawberries (1 qt), trimmed and halved (quartered if large)
1 cup fresh lemon juice
3/4 cup superfine granulated sugar
4 cups water
1 vanilla bean, halved lengthwise, or 1 teaspoon vanilla extract
Blend strawberries, lemon juice, sugar, and 2 cups water in a blender, 1 to 2 minutes (in batches if necessary). Scrape seeds from vanilla bean with tip of a knife into blender (or add extract), then blend with strawberry purйe. If desired, pour through a very fine sieve into a pitcher to remove strawberry seeds, pressing hard on solids. Stir in remaining 2 cups water and serve over ice.