In a small bowl, whisk together the olive oil, lemon juice, red wine vinegar, and Dijon mustard until emulsified. Add the minced garlic, oregano, red pepper flakes, salt, and black pepper, stirring well to combine. Set the dressing aside for a few minutes to allow the flavors to blend and the garlic to mellow.

While the dressing rests, dice the cucumber, halve the cherry tomatoes, dice the bell pepper, thinly slice the red onion, and pit and halve the kalamata olives. Roughly chop the parsley and basil separately, keeping the basil aside to add last to preserve its freshness. Arrange all the prepared vegetables on a cutting board ready for mixing.

In a large bowl, combine the rinsed and drained cannellini beans, kidney beans, and chickpeas. Add the diced cucumber, halved cherry tomatoes, diced bell pepper, sliced red onion, halved olives, and chopped parsley. Toss everything gently to evenly distribute the ingredients.

Pour the vinaigrette over the bean and vegetable mixture and toss thoroughly to coat all ingredients evenly. Gently fold in the fresh basil and crumbled feta cheese just before serving to maintain their delicate flavors. Taste and adjust seasonings as needed.