Dough

• 2 1/4 cups (about 9 5/8 ounces) all-purpose flour, plus more for work surface
• 2 tablespoons granulated sugar
• 2 teaspoons instant or quick-rising yeast (such as Fleischmann’s Rapid-Rise, from one [1/4-ounce] envelope)
• 1 1/2 teaspoons kosher salt
• 2/3 cup whole milk, warmed
• 3 tablespoons unsalted butter, softened

Filling and topping

• 3 ounces (6 tablespoons) unsalted butter, softened
• 3 ounces Parmesan cheese, grated (about 3/4 cup)
• 2 tablespoons finely chopped fresh flat-leaf parsley
• 1 tablespoon finely chopped fresh rosemary
• 1 large garlic clove, grated on a Microplane
• 1/4 teaspoon kosher salt
• 1/4 teaspoon black pepper
• 1 tablespoon unsalted butter, melted
• 1/2 teaspoon flaky sea salt