Heat the olive oil in a large saucepan over medium-low heat. Add the peppers, leek, garlic, salt and turmeric, and cook, stirring occasionally, until the vegetables begin to soften, about 10 minutes.

Tie the parsley, thyme, and bay leaf together with kitchen twine. Add the potato, water, and herb bundle and bring to a boil, reduce the heat, and simmer, uncovered, until the potato is very tender, about 20 minutes.

Discard the herb bundle. Puree the soup in small batches in a blender (keep the lid cracked to allow steam to escape), or in the pot with an immersion blender, until smooth. Return to the pot and reheat. Stir in the vermouth, and season, to taste, with salt and pepper. Serve warm.

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