Light the broiler or grill and roast the peppers, turning, until charred on all slides, about 15 to 20 minutes. Remove and place in a stainless steel bowl with a lid or in a plastic bag and seal. Let the peppers cool in their own juices for 15 minutes.

Remove the peppers and reserve their juices. Carefully peel the peppers: Cut in half lengthwise, remove the seeds, and cut each half into strips about an inch (2 ½ cm) wide.

In the bowl of a food processor, place the basil leaves, garlic and pepper juices. Pulse on and off for a minute or so to puree. Add the toasted hazelnuts and pulse to form a paste. Add the parmesan and a little salt and pepper and pulse to form a thicker paste. Drizzle in the olive oil, pulsing all the while, until the pesto is thick but loose enough to spoon over the peppers as a dressing.

Place the peppers in alternating rows or layers of yellow and red strips, spooning a little pesto over each payer or row. Serve.