How to Make It
Grate 1 garlic clove to yield 1/2 teaspoon. Zest and juice 1 lemon to yield 1 teaspoon zest and 3 tablespoons fresh lemon juice; set juice aside. Stir together mayonnaise, grated garlic, and lemon zest; set aside.
Cut remaining lemon in half, reserving 1 half for another use. Very thinly slice remaining lemon half; cut slices into half-moons, and discard seeds. Smash 2 garlic cloves, and place in a 12-inch skillet; add 1/2 cup oil and lemon half-moons. Cook over low, swirling skillet occasionally, until fragrant and lemon pith is tender, about 5 minutes. Stir in beans, shallot, chile, and reserved 3 tablespoons lemon juice. Increase heat to medium-high, and bring to a simmer. Simmer 1 minute. Transfer mixture to a medium bowl; season with salt and pepper to taste. Let mixture marinate at room temperature 30 minutes. Stir in celery and herbs.
While mixture marinates, heat a grill pan over medium. Lightly brush bread with remaining 1 tablespoon oil. Grill bread until crisp, about 3 minutes per side. Rub remaining garlic clove over one side of each bread slice, and top evenly with bean mixture. Drizzle with any remaining juices in bottom of bowl. Spoon dollops of aioli on each, and garnish with celery leaves.