Cut cauliflower into bite sized pieces, discarding stems.
Thinly slice red onion.
Mix all ingredients, excluding the parmesan, in a large bowl.
Divide evenly between the foil sheets.
Fold into tent packs.
Toss parmesan into resealable bag.
Let fire burn down to coals.
Spread out a two inch layer of coals.
Cook foil packs directly on hot coals for ten minutes.
Remove to indirect (but hot) heat for an additional 30 minutes.
Gently open top of foil packets and sprinkle on parmesan cheese (divided evenly between the two foil packs).
Cook until the parmesan starts to melt (an additional 5 to 10 minutes).
After plating, squeeze a little lemon juice on each serving (optional).