1. Place potatoes in a medium saucepan, and cover with cold water. Add 1 tablespoon salt, and place over high heat. Bring to a boil, and reduce heat to medium. Cook until potatoes are fork tender, 8 to 10 minutes. Using a slotted spoon, transfer potatoes to a colander. Let stand until cool enough to handle, and slice in half lengthwise. Transfer to a large mixing bowl.

2. Raise the heat to high, and add the string beans to the boiling water. Cook until bright green and al dente, about 3 minutes. Drain beans in a colander. Transfer beans to the bowl with the potatoes.

3. Place basil, mint, spinach, pine nuts, garlic, and 3/4 teaspoon salt in the bowl of a food processor. Turn on machine, and slowly add the olive oil. Process until a puree forms. Add the Parmesan cheese and the butter; process until pureed.

4. Pour the pesto over the potatoes and string beans, and toss to combine. Transfer the vegetables to a serving dish, and sprinkle the scallions over the top. Serve warm.