Make the Dough: In the bowl of a stand mixer fitted with a dough hook or paddle attachment, combine the yeast and sugar. Warm the milk on the stove or in the microwave until it reaches 110°F (43°C). Pour the warm milk over the yeast mixture, whisk gently, and cover with a clean kitchen towel. Let it sit for 5-10 minutes until frothy.
Add the softened butter, egg, flour, salt, garlic powder, and rosemary to the bowl. Mix on low speed for 3 minutes until the dough is soft.
Knead the Dough: Continue kneading the dough in the mixer (switch to the dough hook if using the paddle attachment) for 5 minutes, or knead by hand on a lightly floured surface for 5 minutes. If the dough becomes too sticky, add flour 1 teaspoon at a time until it is soft and slightly tacky. The dough is ready when it slowly bounces back when poked.
First Rise: Shape the dough into a ball and place it in a greased bowl. Cover with plastic wrap or aluminum foil and let it rise in a slightly warm environment until doubled in size, about 60-90 minutes.
Prepare the Filling: While the dough rises, mix the softened butter, rosemary, parsley, garlic, and salt together in a medium bowl. Cover and set aside at room temperature.
Assemble the Bread: Punch down the dough to release the air. Transfer it to a lightly floured work surface and divide it into 12 equal pieces, each about ¼ cup of dough. Flatten each piece into a 4-inch circle. Spread 1-2 teaspoons of the filling on each circle and sprinkle with 1 tablespoon of cheese. Fold each circle in half and arrange them in a greased 9×5-inch loaf pan, with the round side up.
Second Rise: Cover the pan with plastic wrap or aluminum foil and let the dough rise again in a slightly warm environment until puffy, about 45 minutes.
Bake: Preheat the oven to 350°F (177°C). Adjust the oven rack to the lower third position. Bake the bread for about 50 minutes, or until golden brown. If the top is browning too quickly, tent with aluminum foil. If desired, brush the top with melted butter and sprinkle with sea salt.
Serve: Cool the bread in the pan for 10 minutes, then transfer to a wire rack. Serve warm.
Storage: Cover and store leftovers at room temperature for up to 2 days or in the refrigerator for up to 1 week. Reheat in a 300°F (149°C) oven for 10-15 minutes or in the microwave until warmed through.