Place potatoes, salt, red wine vinegar, rosemary sprigs, bay leaves, and water to cover in a medium saucepan. Bring to a boil over high; reduce heat to medium-low, and simmer until potatoes are tender when pierced with a fork, about 10 minutes. Drain and place in a single layer on a baking sheet. Cool completely, about 15 minutes.
Meanwhile, heat 1 tablespoon of the olive oil in a medium saucepan over medium-high. Add onion, and cook, stirring often, until tender, about 3 minutes. Stir in garlic and paprika, and cook, stirring constantly, 30 seconds. Add tomatoes and sherry vinegar; cook, stirring often, 10 minutes. Remove from heat, and cool 10 minutes.
Combine tomato mixture and mayonnaise in a food processor; process until smooth, about 1 minute. Set aside.
Heat remaining oil (about 1/4 cup) in a large saucepan over medium-high. Cook potatoes in hot oil, stirring occasionally, until brown and crisp, about 10 minutes. Remove potatoes with a slotted spoon, and drain on paper towels.
Divide potatoes among 6 bowls, and drizzle with some of the Tomato Mayonnaise. Sprinkle with chives, and serve immediately with remaining Tomato Mayonnaise.