Preheat barbecue grill to high heat.

Prepare the garlic for roasting: remove the outer, papery layer and slice off the top to expose the cloves.

Drizzle the garlic with 1/2 teaspoon of olive oil and wrap it tightly in a double-thick square of foil.

Place the foil-wrapped garlic directly on the hot grill rack.

Repeat the garlic-wrapping procedure with the onions, wrapping each onion individually.

Rub the portobello caps, stems, and crimini mushrooms with olive oil, salt, and pepper.

Place the portobello caps, stems, crimini mushrooms and foil-wrapped onions on the grill.

Grill the portobello caps, stems, and criminis until lightly browned, approximately 3 to 5 minutes on each side. Do not overcook.

Remove the portobello caps, stems, and criminis from the grill.

Cut the portobello stems and criminis into 1/4-inch strips and set aside to keep warm.

On the stove or in a pan on the barbecue grill, heat a saute pan until hot.

Add 1 tablespoon of olive oil to the hot saute pan.

Add the roasted garlic and saute for 15 seconds (do not brown).

Reduce the heat to medium-high.

Toss the chicken strips in flour.

Add the floured chicken strips to the garlic mixture in the saute pan.

Season with salt, pepper, and red pepper flakes (optional).

Saute quickly until the chicken is lightly golden brown and begins to stick to the pan.

Add the white wine and butter to the pan, then reduce the heat to medium.

Continue cooking until a light sauce develops, approximately 5 minutes.

Toss in the fresh herbs and continue cooking for 1 to 2 minutes, then remove from the heat.

To assemble the stuffed mushrooms, place the portobello caps on plates.

Sprinkle the inside of each mushroom cap with shredded Parmesan cheese.

Gently toss together the chicken strips, pepper strips, onion strips, and mushroom strips.

Pile the chicken mixture onto each portobello cap.

Add 2 to 3 Parmesan curls to the top of each stuffed mushroom.

Decorate with a basil sprig and serve warm.