Lemon Raspberry Breakfast Rolls

Name: Lemon Raspberry Breakfast Rolls
Ingredients: 1 cup milk (I used 2 percent); 2/3 cup sugar; 1 1/2 tablespoon active dry yeast; 1/2 cup (1 stick) unsalted buttered, softened to room temperature; 2 large eggs; 1/2 teaspoon lemon zest; 1/2 teaspoon salt; 4 1/4 cups all-purpose flour, plus 1/2 cup for kneading, plus more for sprinkling the counter; 1 heaping cup fresh raspberries (if using frozen, do not thaw); 1/3 cup sugar plus 1/2 cup sugar for dusting; 1 teaspoon lemon zest; 1 teaspoon cornstarch; 1/4 cup (1/2 stick) unsalted butter, melted, browned and slightly cooled; 1 1/2 cup powdered sugar; 2 tablespoons lemon juice; 1 tablespoon water