Heat butter and olive oil in a large skillet over medium-high heat. Add onion, carrot and celery and sauté until onions are translucent, about 4 to 5 minutes. Season with Hi Mountain Garlic Pepper. Add acorn squash and cook for 3 more minutes. Add garlic.
Add duck and cook until lightly browned. Add rice and chicken broth. Stir to combine contents of the skillet and cook until hot.
Crack eggs over skillet, keeping yolks intact, if possible. Cover with a lid or foil to cook eggs to desired temperature. For runny eggs, they are done with the top just turns creamy white. Top with Hi Mountain Trail Dust.