Seed and core the peppers, then cut them into 1 1/2-inch wide strips.
Place the pepper strips in a large bowl. Add 1/3 cup olive oil, 1 teaspoon coarse salt, and 1/2 teaspoon freshly ground black pepper; toss until the peppers are evenly coated.
Heat a grill to medium (about 375°F).
Move the peppers from the bowl to the grill, leaving any remaining oil in the bowl. Arrange peppers in a single layer as much as possible.
Grill the peppers until they are blistered and beginning to blacken around the edges on one side, about 10 minutes; use tongs to flip and grill the other side until blistered and soft, about 10 more minutes (about 20 minutes total).
Transfer the cooked peppers back into the bowl with the reserved oil, toss to coat, and cover the bowl with foil to keep warm until ready to serve.
Brush both sides of the bread slices with the remaining 2 tablespoons olive oil.
Grill the bread slices 1–2 minutes per side, until the edges are toasted and the slices are warmed through.
Place toasted bread on a serving board or plate, top each slice with the roasted peppers, and drizzle any remaining oil from the bowl over the crostini. Serve.