To roast peppers, place under or over flame in broiler or on stovetop until skin is blackened. Peel off black skin and discard it.
In a food processor, combine egg yolks, garlic, roasted pepper and basil. Add oil very slowly in a thin stream with food processor running until the ingredients form an emulsion. Store in refrigerator. This may be made one day ahead. Makes 4 cups.
Season tenderloin with salt and pepper and rub with olive oil. Place thyme sprigs on and around meat and let marinate for 30 minutes. Roast on a rotisserie or in a grill over an open flame until internal temperature reaches 120F, about 25 minutes until beef is cooked rare. Let rest for 15 minutes.
To serve, carve into thin slices. Place crostini on plates, top with slices of beef and drizzle with aïoli.