Prepare the Dough: In a large mixing bowl, combine the flour, yeast, sugar, and salt. Add the warm milk, melted butter, and beaten egg, and mix until a soft dough forms.
Turn the dough out onto a floured surface and knead for about 5 minutes, or until smooth and elastic.
Place the dough in a greased bowl, cover with a clean towel, and let it rise in a warm place for about 1 hour, or until doubled in size.
Preheat and Prepare Pan: Preheat the oven to 375°F (190°C). Grease a Bundt pan thoroughly.
Prepare Cheese Mixture: In a small bowl, mix together the cheddar cheese, Parmesan cheese, parsley, garlic powder, and oregano.
Shape the Dough Balls: Punch down the risen dough and divide it into small pieces. Shape each piece into a ball and roll it in the cheese mixture to coat.
Assemble the Bread: Arrange the coated dough balls in the prepared Bundt pan, layering them until all the dough and cheese mixture are used.
Second Rise: Cover the Bundt pan with a clean towel and let the dough rise again for about 30 minutes.
Bake the Bread: Bake in the preheated oven for 25-30 minutes, or until the bread is golden brown and a toothpick inserted into the center comes out clean.
Cool and Serve: Let the bread cool in the pan for 5 minutes before inverting onto a serving plate. Serve warm for a delicious pull-apart experience.