Toast the Sourdough: Preheat your oven's broiler to high, or heat a grill pan over medium-high heat. Arrange the sourdough slices on a baking sheet. Brush both sides lightly with about 3 tablespoons of the extra virgin olive oil. Broil or grill for 2-3 minutes per side, until golden brown and crisp at the edges.
Infuse with Garlic: Once the bread is toasted, take one whole, peeled garlic clove and rub its cut surface vigorously over one side of each warm sourdough slice. The heat from the toast will melt the garlic slightly, infusing it with flavor. Set the anointed toasts aside.
Prepare the Bean Base: In a mini food processor, combine the rinsed cannellini beans, 1 tablespoon of lemon juice, 1 tablespoon of olive oil, and the remaining 2 garlic cloves (minced). Pulse until a thick, rustic puree forms. Season with a few grinds of black pepper. If you don't have a processor, you can mash these ingredients thoroughly with a fork in a small bowl.
Mix the Tomato Topping: In a large mixing bowl, combine the diced tomatoes, sliced basil, diced red onion, chopped Kalamata olives, balsamic vinegar, and lemon zest. Drizzle with the remaining 2 tablespoons of olive oil and gently stir to combine. Let the mixture sit for at least 10 minutes to allow the flavors to meld.
Assemble the Crostini: Spread a thin, even layer of the savory bean puree onto the garlic-rubbed side of each toasted sourdough slice.
Add the Topping: Using a slotted spoon to leave excess liquid behind, spoon a generous amount of the tomato mixture over the bean puree on each toast.
Garnish and Serve: Arrange the finished crostini on a platter. Add one final, light drizzle of extra virgin olive oil over the top, sprinkle with a tiny pinch of flaky sea salt for texture, and serve immediately.