In a small bowl, whisk together olive oil, lemon juice, red wine vinegar, and Dijon mustard until fully emulsified. Stir in minced garlic, oregano, red pepper flakes, and salt and pepper to taste. Set aside for about 10 minutes.

Dice cucumber and bell pepper. Halve cherry tomatoes and thinly slice red onion. Pit and halve Kalamata olives, and chop fresh parsley. Keep basil aside for later.

In a large mixing bowl, combine the drained and rinsed cannellini beans, kidney beans, and chickpeas. Gently fold in prepared vegetables: cucumber, cherry tomatoes, bell pepper, red onion, olives, and parsley.

Pour the dressing over the combined salad ingredients, tossing gently until everything is well coated.

Fold in chopped fresh basil and crumble in feta cheese before serving. Taste and adjust with more salt or lemon juice as necessary.

For optimal flavor, refrigerate the salad for 30 to 60 minutes before serving.