Preheat the oven to 355°F/180°C. Line a large baking sheet with parchment paper. Wash the eggplants, zucchinis, and red peppers. Prick each vegetable several times with a fork to prevent splitting during roasting.
Arrange the vegetables in a single layer on the prepared sheet. Roast for 45 to 50 minutes, until softened and slightly charred. Remove from the oven and let cool slightly. Peel the peppers and discard the seeds. Slice the zucchinis in half lengthwise, remove the seeds, and scoop out the flesh. Peel the eggplants. Place the eggplant and zucchini flesh in a colander and let drain for 15 to 20 minutes to remove excess liquid.
Finely chop the drained eggplant and zucchini on a cutting board, sprinkling lightly with salt to help draw out flavor. In a large mixing bowl, combine the chopped vegetables with the red onion. Season with salt and pepper, add the sunflower oil, and mix thoroughly until smooth and cohesive.
Refrigerate for at least 30 minutes before serving. Serve cold, spread on crusty bread or alongside fresh tomatoes.