Preheat oven to 400°F. Lightly coat an 8-inch-square baking dish with cooking spray.
Heat 1 tablespoon oil in a large skillet over medium heat. Add onion; cook, stirring occasionally, until softened, about 4 minutes. Add garlic; cook, stirring, until fragrant, about 1 minute. Stir in spinach and cream cheese; cook, stirring constantly, until the cream cheese is melted and the vegetables are coated, about 2 minutes. Transfer to a medium bowl and let cool slightly, about 5 minutes.
Add beans, chicken, feta, Parmesan, dill, lemon zest and pepper to the spinach mixture; stir until fully combined. Spoon into the prepared baking dish.
Cut each phyllo sheet in half crosswise. Place 1 half sheet on top of the spinach mixture; brush with some of the remaining 2 tablespoons oil. Repeat the process with the remaining phyllo sheets and oil, stacking the sheets. Score the phyllo into 2-inch squares with a sharp knife. Bake until golden brown on top, about 25 minutes. Let cool for 10 minutes before serving.
