Grilling gives lettuce charred edges that add extra flavor while keeping the inside nice and crunchy.
Heat a grill or grill pan to medium-high. Clean and lightly oil hot grill. In a small bowl, whisk together buttermilk, mayonnaise, and vinegar. Stir in basil and chives; season with salt and pepper. (To store, refrigerate in an airtight container, up to 3 days.)
Brush both sides of bread with oil and grill, flipping once, until toasted, 3 minutes. Rub with garlic, season with salt, and cut into cubes.
Grill lettuce, cut side down, until charred in spots, about 3 minutes. Serve warm, topped with dressing and croutons.
Cooking lettuce intensifies its natural sweetness.