Slice baguette into ½-inch rounds. Toast at 400°F for 5–6 minutes, flipping once, until golden and crisp.
While warm, rub cut side of whole garlic clove across each slice.
Combine black-eyed peas, tomato, red onion, basil, minced garlic, olive oil, balsamic, lemon juice, salt, and pepper in a bowl.
Taste and adjust seasoning.
Spoon 1 tbsp topping onto each toast just before serving. Serve extra topping in a small bowl alongside.