Brown Butter Cinnamon Rolls

Name: Brown Butter Cinnamon Rolls
Ingredients: 1¼ cup (2½ sticks) unsalted butter; 3 tablespoons water; 3 tablespoons whole milk; 2 teaspoons all-purpose flour; ¼ cup brown butter; 1/3 cup whole milk; 1 large egg (at room temperature); 2 cups all-purpose flour; 1 1/2 teaspoons instant dry yeast; 1 tablespoon granulated sugar; 1 teaspoon kosher salt; ½ cup brown butter (melted); ¾ cup brown sugar; 2 teaspoons cornstarch; 2 tablespoons ground cinnamon; pinch fine sea salt; 3 tablespoons brown butter (softened); 2 oz cream cheese (softened); 1 cup powdered sugar (sifted); ½ teaspoon vanilla paste or extract