Heat oven to 400° F. On a rimmed baking sheet, toss the bread with the oil and ¼ teaspoon each salt and pepper. Bake, tossing once, until golden, 7 to 9 minutes. Let cool.
In a large bowl, whisk together the buttermilk, mayonnaise, parsley, garlic, ½ teaspoon salt, and ¼ teaspoon pepper. Add the lettuce, radishes, shallot, and croutons and toss to coat.