Preheat the broiler on high with the oven rack right underneath it.
Place the peppers on a foil-lined sheet pan and broil until charred all over, turning the peppers every 2-3 minutes. It will take 10-12 minutes.
Transfer the peppers to a bowl and cover it. Let the peppers sit for 15 minutes before rubbing off their skins, removing the seeds and cutting them into 1-inch wide strips.
Turn off the broiler and preheat the oven to 400 degrees F.
On a sheet pan, toss the bread with 1 tablespoon olive oil, 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper. Spread the bread into a single layer and toast it in the oven until golden brown, about 12-15 minutes.
For the vinaigrette, whisk together garlic, mustard, honey, oregano, red pepper flakes, 1/2 teaspoon salt, 1/4 teaspoon black pepper, red wine vinegar and 1/4 cup olive oil in a small bowl.
To assemble the salad, combine the peppers, olives, cucumbers and onions in a large bowl. Drizzle in the vinaigrette, stirring to combine.
Fold in the toasted bread, shaved Parmesan and basil leaves.