Preheat oven to 350. Wash and clean Brussels. Using a simple slicer or mandoline shave Brussels to about 1/8 inch.
In large bowl toss together brussels, cheddar, flour and salt and pepper (use other dried herbs if desired) until thoroughly combined. Move mixture to an 8x8 baking dish, packing down. Pour cream over the top.
In the now empty bowl crush the croutons until very fine. Add the Parmesan cheese and the oil and toss to mix. Spread, evenly, over the brussels.
Bake, uncovered, for 30-40 minutes or until brussels are tender and the topping is golden.