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Preheat oven to 42℉/220C
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Place the pepper halves, whole chile peppers, and cut tomatoes in a large mixing bowl together with the shallots, onion and garlic cloves. Drizzle with 6 tablespoons of olive oil and season with sea salt and black pepper. Place them skin side up in a large roasting pan in a single layer if possible and roast for 45 minutes to an hour, until the pepper and tomato skins are crinkled and lightly charred and everything is really soft.
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About halfway through the roasting, check the shallots and garlic and remove if their already softened. The garlic should be creamy inside its skin.
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Remove the vegetables from the oven, cover the pan with a towel and let the peppers and tomatoes cool down enough to handle them. Peel and discard their skins. Use gloves when handling the hot peppers, if using. Remove their stems, slit them down the middle, and scrape out their seeds. Squeeze the garlic cloves from their skins. Place the skinned tomatoes, peppers, garlic and shallots in a medium pot with the smoked paprika, cayenne (if using), fresh herbs, and vegetable stock. Bring to a boil, then lower the heat to medium and cook, uncovered, for about 15 minutes.
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Working in batches, puree the soup in the pot with an immersion blender or in a food processor. Transfer the soup back to the pot, taste, and adjust the seasoning with additional salt and pepper. Stir in the vinegar, adding more if needed to balance out the acidity and the sweetness of the peppers. If the soup is too thick add more stock or water.
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Preheat a skillet over a medium flame, and add 2 tablespoons of olive oil. Stir the minced shallot until translucent. Add the corn kernels, salt and pepper, and the thyme. Cook for 2 minutes and remove.
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To serve, place a small pile of the corn in the center of a warmed soup bowl, pour the soup around, drizzle with the remaining olive oil, and sprinkle with a little crumbled feta.