1. Place potatoes in a large pot with enough water to cover by several inches. Bring to a boil over high heat, add 1 tablespoon salt, and lower to a gentle boil. Cook until potatoes are tender when pierced with a knife, about 15 minutes. Drain into a colander. Using gloves or paper towels to protect your hands, slice hot potatoes into 3/4-inch-thick rounds. Drizzle with vinegar, and set aside.

2. Fill a large bowl with ice and water. Fill a large straight-sided saute pan with water, and place over high heat. Bring to a boil; add 1 teaspoon salt and the asparagus. Cook until just barely tender, about 3 minutes. Transfer to ice bath until cool. Dry, and cut diagonally into 2-inch pieces. Place peas in boiling water, and cook until bright green, about 1 minute. Drain into a colander; transfer to ice bath to stop cooking. Dry on towels.

3. Place mint, basil, mayonnaise, lemon juice, remaining teaspoon salt, and pepper in the bowl of a food processor, and pulse until smooth. Transfer to a large bowl, add reserved potato mixture, asparagus, peas, sugar snap peas, and fennel, and toss to combine. Garnish with basil and mint leaves, and serve.