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—I like to let it sit for a few minutes while prepping the vegetables so the garlic flavor can mellow slightly and the spices fully hydrate.
While the dressing rests, prepare all the vegetables for the salad. 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 fresh parsley and basil separately (I keep them separate at this stage since basil bruises easily and benefits from being added last). Place all prepared vegetables on a clean cutting board so they're ready to go.
In a large bowl, combine the rinsed cannellini beans, kidney beans, and chickpeas. Add the diced cucumber, halved cherry tomatoes, diced bell pepper, sliced red onion, halved olives, and the parsley. Toss everything together gently to distribute the vegetables evenly throughout the beans. The beans will provide structure and hold everything together nicely.
Pour the vinaigrette from Step 1 over the bean and vegetable mixture and toss thoroughly, ensuring the dressing coats everything evenly. Gently fold in the fresh basil and crumbled feta cheese just before serving—adding them at the end preserves their delicate flavors and prevents the basil from darkening. Taste and adjust seasonings if needed.