Arrange the eggplant slices on a large plate or baking sheet. Sprinkle with salt and let them sit for 30 minutes to draw out excess moisture. Pat dry with a paper towel.

On a lightly floured surface, roll out the puff pastry into a rectangle, about ⅛ inch thick. Slice into three equal portions (or keep whole for a larger tart).

Arrange the mozzarella slices evenly over the pastry, leaving a ½-inch border. Layer the salted eggplant slices on top. Gently fold in the edges of the pastry to create a rustic border.

Brush the eggplant with olive oil and scatter the cherry tomato slices over the top.

Brush the pastry edges with the beaten egg and sprinkle with sesame seeds. Transfer to a parchment-lined baking sheet and bake in a preheated 350°F (180°C) oven, fan setting, for 30–35 minutes, or until golden brown and crisp.

Remove from the oven and immediately sprinkle with crumbled Bulgarian feta and fresh basil leaves. Serve warm or at room temperature.