Preheat your oven to 375 degrees F.
Carefully slice your acorn squash unto ¾ inch think rounds and scoop out the inside to form a perfect hole for your egg mixture.
In a large cast iron skillet over medium high heat brown your sausage and once done set the sausage aside. Being careful not to burn yourself, wipe out the excess sausage grease from the inside of your skillet.
In a small bowl whisk your eggs and milk together until thoroughly combined. Then mix in your shredded parmesan cheese. Season with salt and pepper.
Return your skillet to a medium high heat. Brush one side of your acorn squash slices with olive oil and season with salt, pepper and smoked paprika. Place the squash slices in the skillet seasoned side down. Brush the tops with olive oil and season the same way.
Spoon a generous helping of the sage sausage into the hole of your acorn squash, then cover with your egg mixture until the hole is full. Sprinkle we extra parmesan cheese.
Allow your acorn squash eggs in a hole to cook in the skillet for 5 minutes then transfer the entire skillet to your preheated oven. Cook until the squash is tender and the eggs start to firm up, roughly 15 minutes.
Adjust the oven temperature to high broil, and while watching carefully, allow them to cook until nice and golden brown on top, roughly 3 minutes.
Top with additional parmesan cheese and enjoy.