Prepare basting oil: mix olive oil, lemon juice, salt & pepper and whisk together.
Rinse head of cauliflower and remove leaves. Cut off any existing stalk so cauliflower sits flat on cutting board when turned upright.
With a large sharp knife, slice head of cauliflower right down the middle. Cut into 1 inch steaks and lay on baking tray. Note: each slice will not be usable as a steak – the “steaks” will be cut from the center of the head where the core unites all the florets. Place the larger florets that fall away in a large plastic resealable bag. Set aside.
Using a basting brush coat both sides of “steaks” with basting oil. Pour remaining oil over florets in plastic bag, seal and shake until coated. Grill “steaks” and florets on medium heat for 5-7 minutes on each side. Keep an eye on them so they don’t burn.
During last 2 minutes of grilling, sprinkle cauliflower with Parmesan cheese. Remove from grill and serve immediately.