Heat vegetable oil in an 8-inch skillet over medium-high heat. Fry leeks in batches until golden brown, about 2 minutes per batch, and transfer to a paper towel-lined plate.
In a medium bowl, whisk together vinegar, salt, pepper, and oil. Add cucumber, tomatoes, and kalamata olives and toss to combine.
Spread out Romaine on a large platter and cover with dressed vegetables. Top with grape leaves, chickpeas, leeks, and feta and serve.