Prepare the Dough:

• In a large mixing bowl (or the bowl of a stand mixer), combine the all-purpose flour, instant yeast, granulated sugar, and salt. Whisk to combine.
• In a separate medium bowl, whisk together the warm milk, warm water, melted butter, and room-temperature egg.
• Pour the wet ingredients into the dry ingredients. Mix with a wooden spoon or spatula (or with the dough hook attachment of a stand mixer on low speed) until a dough begins to form.
• Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, or until the dough is smooth and elastic. Alternatively, knead with the dough hook on low speed for 5 minutes.

First Rise: Lightly grease a large bowl. Place the kneaded dough in the greased bowl, turning it to coat all sides. Cover the bowl with plastic wrap or a clean kitchen towel. Let the dough rise in a warm place, free from drafts, until doubled in size, about 1 hour.

Prepare the Cheese Filling: While the dough is rising, prepare the cheese filling. In a medium bowl, combine the shredded cheese, grated Parmesan cheese, dried oregano (if using), and garlic powder (if using). Stir well to combine. Set aside.

Shape the Buns:

• Once the dough has doubled, gently punch it down to release the air. Turn the dough out onto a lightly floured surface. Divide the dough into 12 equal pieces.
• Working with one piece at a time, flatten it into a small circle (about 3-4 inches in diameter).
• Place 1-2 tablespoons of the cheese filling in the center of the dough circle.
• Bring the edges of the dough up around the cheese filling and pinch them together tightly to seal, forming a ball.
• Place the shaped bun, seam-side down, on a baking sheet lined with parchment paper.
• Repeat with the remaining dough pieces and filling, spacing the buns about 1-2 inches apart on the baking sheet.

Second Rise: Cover the buns loosely with a kitchen towel or lightly greased plastic wrap. Let them rise in a warm place for another 30 minutes, or until puffy.

Preheat Oven: While the buns are rising for the second time, preheat your oven to 375°F (190°C).

Brush and Top Buns: Gently brush the tops of the risen buns with some of the melted butter. If desired, sprinkle with the additional 1/4 cup of shredded cheese and the dried herbs.

Bake: Bake in the preheated oven for 18-20 minutes, or until the buns are golden brown on top and sound slightly hollow when tapped.

Finish and Serve: Remove the buns from the oven and brush them again with the remaining melted butter while they are still warm. Let them cool slightly on the baking sheet before serving. Serve warm.