Line a rimmed cookie sheet with tinfoil. Wash peppers, remove stickers and place whole, intact peppers on the cookie sheet.
Broil peppers close to the broiler, like on the second rack location in the oven.
Char the peppers until they are black on all sides. Using tongs, turn the peppers every few minutes as they char. The charring will take about 45 minutes to get all parts of the pepper.
Remove the cookie sheet from the oven and cover it with tinfoil and let the peppers cool.
When cool enough to handle, start to peel the charred skin off the peppers so all of the black skin is removed and only the pepper pieces are left. Also remove all of the seeds from the peppers. Discard charred skin, seeds and stems.
Slice all of the prepped, cleaned pepper pieces into strips and arrange the pieces on a plate. Top the pepper slices with the basil and capers.
Drizzle the olive oil over the peppers. Drizzle the balsamic glaze over the peppers. Season with salt and pepper, but do not stir. Top with crumbled feta. Serve at room temperature.