Cut peppers in half, removing ribs and seeds. Place cut side down onto a baking sheet and drizzle with oil. Broil on high on the top rack of your oven, until peppers are blistered. Place into a bowl and cover with plastic wrap. Allow to steam for about 15 minutes, then remove skins.

Cut peppers into short, thin strips. Transfer strips to a medium bowl and toss with pepper and ⅔ cup olive oil. Cover and marinate in the refrigerator for at least 3 hours and up to 8.

Heat oven to 325º. Brush baguette slices with oil on both sides and place on a baking sheet. Bake until dry and lightly toasted, about 15 minutes. Pierce half of garlic clove with a fork and rub the crostini while they’re still warm. Repeat with the remaining half clove when needed. This step can be performed one day ahead of time. If preparing in advance, allow baguette slices to cool before storing in an airtight container.

Spread a small amount of goat cheese onto each baguette slice. Top with a few strips of peppers and place on serving platter. Scatter basil over the top and serve.