Preheat oven to 375°F. Line a rimmed baking sheet with parchment.
Unroll crescent dough onto the sheet. Press seams and shape into an even rectangle.
Brush dough lightly with olive oil. Bake until golden, 12–14 minutes. Cool completely on the pan.
Beat cream cheese and Greek yogurt until smooth and fluffy.
Stir in lemon zest, lemon juice, garlic, dill, oregano, salt, and pepper.
Spread the herbed mixture over the cooled crust, reaching the edges.
Top evenly with cucumber, tomatoes, bell pepper, red onion, and olives. Press gently to set.
Scatter feta and parsley over the vegetables. Chill 10–15 minutes for cleaner slices.
Cut into squares and serve cold or at room temperature.