Preheat grill to medium-high. Season chicken with salt and pepper and drizzle with oil. Grill chicken until cooked through, 5 to 6 minutes per side. Let stand 5 minutes, then slice on the bias.
Pulse bell peppers, chipotle pepper, garlic, almonds, and oregano in a food processor until coarsely chopped. Drizzle remaining 2 tablespoons oil and process until combined. Season with salt and pepper.
Spread each slice of bread with pesto. Layer with sliced chicken, escarole, and cheddar.