In a food processor, combine basil, garlic, egg yolks, red pepper flakes, salt & pepper. Pulse.
Set the food processor to a low setting and slowly pour in olive oil. Continue to run processor on low until the aioli has reached your desired consistency.
Preheat grill to medium heat.
Place potatoes in a saucepan and cover with water. Add salt.
Bring to a boil. simmer for 8-9 minutes.
Simmer for 8-9 minutes. Potatoes should be easily pierced with a fork.
Strain and run potatoes under cold water to prevent further cooking.
Toss potatoes in olive oil with salt & pepper.
Grill for 5-7 minutes or until potato skins are slightly charred.
Serve with basil aioli.