Step 1: Prepare the Dough

1. In a food processor, combine the flour, sugar, and yeast. Pulse a few times to mix.
2. With the motor running, gradually add ice-cold water, followed by olive oil and salt. Process until the dough forms a smooth ball. (If mixing by hand, stir all ingredients together in a bowl and knead for about 8-10 minutes until soft and elastic.)
3. Transfer the dough to a lightly oiled bowl, cover with plastic wrap, and refrigerate for 24 hours. This slow fermentation enhances the flavor and texture.

Step 2: Make the Eggplant Topping

1. Prepare the tomatoes: Pulse the canned tomatoes in a food processor until slightly chunky. Alternatively, crush them by hand. Set aside.
2. Heat 2 tablespoons of olive oil in a large pan over medium heat. Add half of the eggplant, season with salt and pepper, and cook for 10 minutes until browned and soft. Remove and set aside.
3. Add remaining eggplant, bell pepper, and 1 tablespoon of olive oil to the pan. Cook for another 10 minutes, stirring occasionally.
4. Stir in garlic, paprika, and chile flakes, cooking for 1-2 minutes until fragrant.
5. Return the reserved eggplant to the pan, add the tomatoes, and simmer for 10 minutes, stirring occasionally until thickened.
6. Remove from heat, stir in chopped parsley, and let cool.
7. Once cooled, fold in the crumbled feta. Set aside.

Step 3: Shape the Pide

1. Place a baking stone or steel in the oven and preheat to 550°F (290°C) for at least 1 hour. (If using a regular baking sheet, preheat the oven to 475°F (245°C).)
2. Remove the dough from the refrigerator and let it come to room temperature (about 30-45 minutes).
3. Divide the dough into six equal pieces and cover with a damp towel to prevent drying.
4. On a lightly floured surface, roll each piece into a 14×5.5-inch (35x14cm) oval. (If the dough resists stretching, let it rest for 5 minutes to relax the gluten.)
5. Place the dough ovals on parchment paper for easy transfer.

Step 4: Assemble and Bake

1. Lightly brush each dough oval with olive oil.
2. Spread about 1/2 cup of the eggplant filling evenly over each oval, leaving a 1/2-inch (1.3cm) border on the edges.
3. Fold the long edges inward, slightly overlapping the filling, and pinch the ends to create a canoe shape.
4. Brush the folded edges with olive oil.
5. Transfer the pide (with parchment) onto a pizza peel and slide onto the preheated baking stone. If using a baking sheet, place directly on the sheet.
6. Bake for 10-15 minutes, until golden brown and crisp.
7. Garnish with extra chopped parsley, slice, and serve hot.