Beef Pirozhki
1 (.25 ounce) package active dry yeast 1 cup warm milk (110 degrees F) 1 large egg, beaten 1 large onion, finely diced 1 tablespoon butter 1 tablespoon olive oil 1 teaspoon kosher salt 2 pounds ground beef 2 tablespoons grated Parmesan cheese 2 tablespoons melted butter 2 teaspoons dried dill weed 2 teaspoons kosher salt, or more to taste 2 teaspoons white sugar 3 cups all-purpose flour, or as needed 4 cloves garlic, minced vegetable oil for frying ¼ cup shredded sharp Cheddar cheese ½ teaspoon freshly ground black pepper ½ teaspoon oil, or as needed ⅓ cup chicken broth