Preheat oven to 350°F. Toss together bread, oil, and garlic on a baking sheet. Season with salt and pepper. Bake, stirring once, until golden brown and crisp, 10 to 12 minutes. Cook carrots in boiling salted water in a medium saucepan over high heat until crisp-tender, 2 to 3 minutes. Drain and run under cold water until cool. Gently toss together lettuce, shredded chicken, peas, fennel, croutons, carrots, and vinaigrette in a bowl. Season with salt and pepper