In a 5-quart pot, heat the olive oil and onion over medium-high heat. Cook, stirring frequently, until the onion softens. Add in the garlic, red pepper, and the chopped stems of the chard. Cook for another few minutes, or until the garlic is fragrant.
Add in the chopped tomatoes, water, chipotle pepper, and smoked paprika. Bring the pot to a simmer and let it cook for 15 minutes, or until the vegetables are all soft. Use a blender or an immersion blender to puree the soup (if using a regular blender, let the soup cool first, as hot liquids will expand in the blender and can be dangerous).
Cut the chard greens into ribbons and add them into the pureed soup. Bring it back to a simmer and cook until the chard is soft. Taste and adjust salt as needed. Serve warm, sprinkled with goat cheese, if desired.
