Berry Bagel Puffs

Name: Berry Bagel Puffs
Ingredients: 1 1/2 cups warm water; 2 tablespoons sugar, plus 2 teaspoons; 2 tablespoons plus 2 teaspoons sugar; 4 1/4 to 4 1/2 cups all-purpose flour, plus more for kneading; One 1/4-ounce package dry active yeast; 2 teaspoons kosher salt; 8 ounces fresh strawberries, chopped; 6 ounces fresh blueberries; 8 ounces cream cheese, softened; 2 tablespoons strawberry jam; 1 large egg; 2 tablespoons turbinado sugar; For filling variations, see recipe below; Four 6-ounce packages blackberries, divided; 3/4 cup sugar; 3 tablespoons instant tapioca; 1 tablespoon water