In a small nonstick pan, heat up the olive oil on high heat. Add the mushrooms and cook for 1-2 minutes. Add the spinach and cook for 1 minute. Add the garlic and cook for 1-2 more minutes. The vegetables should be wilted and much smaller in size. Add more oil if necessary. Reduce heat to medium high and add broccoli. Mix in about ¼ teaspoon each of salt and pepper and 1 teaspoon of garlic herb seasoning. Remove from pan and set aside.
In the same pan, heat up the cream cheese, cheddar, and mozzarella on low until they are all melted and combined. Slowly add in the milk while whisking. It should end up pretty thick. Mix in the vegetables. Add ¼ teaspoon each of salt and pepper and 1 teaspoon garlic herb seasoning and set aside.
Cut each chicken breast in half widthwise so that you are left with 4 thin breasts (cutlets). Cover with plastic wrap and pound with a rolling pin or meat pounder. Season on both sides with the remaining salt, pepper, and garlic herb seasoning.
Set out 3 shallow bowls. In one, mix together flour, flax meal, onion powder, and garlic powder. In another, beat the eggs. In the third, put the breadcrumbs.
Scoop as much filling as you can into each cutlet (3-4 tablespoons). It's okay if there are some exposed parts of filling. Roll the chicken so that the filling is inside.
Cover each chicken roll first in the flour mixture, then the egg, and then the breadcrumbs. Place in the prepared baking dish. Optional but recommended--spray olive oil on top of the chicken rolls. This keeps the breadcrumbs from drying out in the oven.
Bake for 18-20 minutes. The top should be golden brown and a meat thermometer should read 165 degrees Fahrenheit.
Optional--if you have any leftover filling, heat it up on low heat and add more milk while whisking constantly so that it thins out. This will create a sauce for your chicken rolls!