Heat a large Dutch oven over medium-high heat. Add oil; swirl to coat. Add onion; sauté 6 minutes. Stir in rind, rosemary, salt, and 1/4 teaspoon pepper; cook 1 minute. Stir in stock, 2 cups water, and potatoes; bring to a boil. Reduce heat to low; cover and simmer 10 minutes. Stir in chard and beans; simmer 10 minutes. Stir in cherry tomatoes.
Fill a skillet two-thirds full with water; bring to a boil. Reduce heat; simmer. Add vinegar. Break each egg into a custard cup, and pour each gently into pan; cook 3 minutes or until desired degree of doneness. Carefully remove eggs from pan using a slotted spoon. Ladle 1 1/2 cups soup into each of 4 bowls; top with a poached egg. Sprinkle with remaining 1/8 teaspoon pepper.