Spray a 9x13 inch casserole dish or eight small ramekins with cooking spray. Use whichever you have on hand. Sprinkle half of the stuffing mix in the bottom of the dish, creating an even layer.
Heat the olive oil in a medium saucepan over medium heat. Add portobello mushrooms. Stir to coat mushrooms in oil. Sauté until mushrooms release their juices, about 5 minutes. Drain excess moisture off and remove mushrooms from heat.
Sprinkle half the mushrooms over the stuffing mix in the casserole dish, then sprinkle half the parmesan cheese over the mushrooms.
Sprinkle the rest of the stuffing mix over this, followed by the rest of the mushrooms and the rest of the cheese.
Whisk together milk, eggs, and basil. Pour this mixture over the top of the casserole. Gently press the strata mixture down so that everything is moistened by the milk mixture.
Cover and refrigerate for 2-24 hours (overnight is best!).
Remove casserole from fridge 30 minutes before you're ready to bake. Preheat oven to 350 degrees, then bake the casserole, uncovered, for 30-40 minutes or until it no longer jiggles and a knife inserted in the center comes out clean.
Serve immediately and dig in!