Place oven rack to the highest position and turn on the broiler. Line a baking sheet with foil. Place whole peppers on the sheet about 2 inches apart.
Broil the peppers until the skin starts to blister and blacken. Using tongs, rotate peppers a quarter turn until all sides are charred, about 5 minutes each side. The peppers should be slightly collapsed and soft. The whole process should take about 20 minutes.
Remove from the oven and place them on a cutting board. Cover peppers with a large bowl or pot to steam them, about 15 minutes.
While the peppers are steaming, prepare the dressing. In a large bowl, add the olive oil, balsamic vinegar, oregano, garlic, red pepper flakes, salt and pepper. Whisk to combine.
When peppers are cool enough to handle, slice them vertically, and spread them open to make a long strip. Remove the stem and seeds. Flip the pepper over and remove charred skin. It should peel off easily.
Cut peppers into ¾-inch strips and place them in the bowl of dressing. Add fresh-cut basil and toss to coat. Taste for seasoning and add more as needed.
At this point, you can serve the peppers right away and top with pine nuts, olives, and vegan feta, OR you can let the peppers marinate in their dressing for an hour or more. Just cover and place in the fridge after tossing. Add the toppings when you are ready to serve. Enjoy!
Notes
Vegan Feta - If you can't find it, use vegan mozzarella or shaved vegan parmesan (Violife has a tasty one).