1. Preheat oven to 375 degrees. Lay 1 sheet phyllo on a work surface, and, with a pastry brush, brush lightly with olive oil. Stack 6 more phyllo sheets on top, brushing each with oil. Cut phyllo in half lengthwise.

2. In a medium bowl, mix ratatouille, breadcrumbs, and feta; season with salt and pepper. With a spoon, spread mixture lengthwise down center of each phyllo half. Fold one side of each phyllo half over mixture and roll into a log. Cut each log into 6 equal pieces and arrange on a parchment-lined rimmed baking sheet.

3. In a small bowl, combine egg yolk with 1 teaspoon water. Brush tops and sides of each piece with yolk mixture. Bake until phyllo is golden brown, 15 to 20 minutes. Let cool slightly before serving.