Preheat the broiler, and place the rack about 6 inches from the heat source. Line a rimmed baking sheet with aluminum foil. Place the peppers on the foil, and place the baking sheet under the broiler.As the side facing the heat bubbles and starts to blacken, after about 2 minutes, turn the pepper to the next side. After about 4 turns and 8 minutes, the peppers should be blistered all over.
Place the peppers in a bowl, (then change the heat in the oven to 425 F and place a baking sheet in the oven), cover with a dishtowel and let them steam.
After about 5 minutes, remove the dish towel, and when they cool enough to handle, peel off the skin and pull them apart so you can remove the seeds and core. Cut the peppers into pieces just the right size to fit in the crostini slices.
While the peppers are cooling, adjust the oven to 350 F. Line a rimmed baking sheet with foil and spray with nonstick spray. Lightly spread each of the baguette slices with the butter, and season with salt and pepper. Place the bread on a baking sheet and toast for 3 minutes, until just barely firmed up. Set aside on the baking sheet
While you are toasting the crostini, in a mini chopper or food processor, puree the basil with 1/4 cup of the olive oil and salt and pepper to taste until well blended. If you don’t have a food processor just finely mince the basil and shake it with the oil in a small container.
Place a square of roasted pepper on each crostini and drizzle over some of the basil oil.
Notes
Make Ahead
You can make all of the components ahead of time. Keep the basil oil and peppers in the fridge, and the crostini in an airtight container at room temperature. Assemble just before serving.