Preheat broiler to high with rack 6 in/15 cm from heat (or heat a grill pan over medium-high). Arrange bread on a baking sheet and brush both sides with 3 tbsp oil. Broil/grill 2–3 min per side until golden and crisp at the edges.
Rub the warm toasts on one side with 1 peeled garlic clove; set aside.
Bean base: In a mini food processor, pulse beans, lemon juice, 1 tbsp oil, and remaining 2 minced garlic cloves to a thick, rustic purée. Season with black pepper.
Tomato topping: In a large bowl, combine tomatoes, basil, red onion, olives, balsamic, and lemon zest. Drizzle with 2 tbsp oil and gently stir. Rest 10 min; if very juicy, drain briefly in a colander.
Spread a thin layer of bean purée on each toast.
Using a slotted spoon, top with tomato mixture.
Drizzle evenly with the remaining 1 tbsp oil, sprinkle a tiny pinch of flaky sea salt, and serve immediately.