Preheat your oven to 350 degrees.
Add about 1 Tbsp olive oil in a large, oven-safe, non-stick pan and heat over medium heat.
Add the sliced onions, season with salt & pepper, and sweat until the onions turn translucent. Add the balsamic vinegar and toss to coat.
Bump the heat down to medium low and slow caramelize the onions, tossing occasionally with a wooden spoon.
Once the onions are caramelized, put them in a bowl and set aside with the other prepared ingredients.
Add the sausage to the pan and cook over medium heat until beginning to brown.
Add the mushrooms, season lightly with salt & pepper, and sauté. If the sausage is lean, you may need to add more olive oil to the pan.
Add the bell pepper, caramelized onions and cherry tomatoes, a pinch more each of salt & pepper, and sauté for 1-2 minutes, tossing the ingredients together.
Turn the burner off, add the grated cheese evenly over the sausage mixture, and add the eggs one at a time on top of that. It's best to crack all the eggs ahead of time into a bowl to prevent egg shells from sneaking in.
Season the eggs with salt & pepper and put the pan into your 350 degree oven until the eggs are done to your liking. The length of time on this depends entirely on your oven, whether it's convection or not etc.. So I prefer to open the door every few minutes and give the pan a shake (wearing an oven mitt, of course). When the white has set up and the yolks move slightly when shaken, that's a perfect, semi-soft egg (my preference).
Top with chopped parsley, scoop each egg, as well as the sausage and veggies they sit on, onto a plate and serve.