Eggs with Basquois Piperade - Fresh-Pressed Olive Oil

Ingredients

• 1 red bell pepper
• 1 green, orange, or yellow bell pepper, or another red one
• 3 tablespoons extra virgin olive oil
• 1 small onion, peeled and diced
• 2 cloves garlic, peeled and minced
• 1 pound red ripe tomatoes, peeled and chopped (reserve juices)
• 1 small zucchini, cubed (optional) Coarse salt (kosher or sea)
• 1 teaspoon piment d'Espelette (see Note below), or to taste
• 1 teaspoon sugar or honey (optional)
• 1 teaspoon red wine vinegar or fresh lemon juice, or to taste (optional)
• 1 tablespoon extra virgin olive oil, plus extra for drizzling
• 4 large eggs, thoroughly beaten
• 1 tablespoon minced fresh chives or flat-leaf parsley
• Country-style bread, preferably toasted or grilled, for serving