In a large mixing bowl, whisk together the flour, yeast, sugar, and salt. Pour in the warm milk, melted butter, and beaten egg. Stir until a soft dough begins to form.
Turn the dough out onto a lightly floured surface and knead for about 5 minutes until the dough becomes smooth and elastic.
Place the dough into a greased bowl, cover with a clean towel, and allow it to rise in a warm place for about 1 hour, or until doubled in size.
Preheat your oven to 375°F (190°C). Grease a Bundt pan generously.
In a small bowl, combine the cheddar cheese, Parmesan cheese, parsley, garlic powder, and oregano. Mix until evenly combined.
After the dough has risen, punch it down and divide it into small, bite-sized pieces. Roll each piece of dough in the cheese mixture to fully coat it.
Layer the cheese-coated dough balls into the greased Bundt pan until all the dough and cheese mixture is used up.
Cover the Bundt pan with a clean towel and let the dough rise again for 30 minutes.
Bake the bread for 25-30 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Once baked, allow the bread to cool in the pan for 5 minutes before carefully inverting it onto a serving plate.
Serve the Cheesy Bundt Bread warm, letting guests pull apart the individual pieces. Enjoy!