Place the peppers on a baking sheet and roast in a preheated 400°F (200°C) oven until the skins blister.
Place in a paper bag and allow to steam for 20 minutes.
Remove from bag and peel away the skin.
Cut into quarters, remove seeds.
In a food processor or blender, blend 1/4 cup (60 ml) of oil, basil, garlic, nuts and cheese.
With the machine running, slowly pour in the remaining oil.
Grill the quartered peppers over medium heat for 6 minutes.
Place on serving plates and top with sauce.