How to Make It
Place the potatoes and 1 tablespoon salt in a large pot. Add cold water to cover by 2 inches. Bring to a boil, reduce heat to a simmer, and cook until tender, about 20 minutes. Drain and set aside until cool enough to handle.
Heat oven to 400° F. Rinse the chicken, pat dry with paper towels, and place in a foil-lined baking dish.
Whisk the mayonnaise and 2 tablespoons of the pesto in a small bowl. Spread evenly over the top of each chicken breast.
Bake until the chicken is cooked through, about 10 minutes.
Leave the chicken in oven and turn on broiler. Broil until golden brown, about 3 minutes.
Peel the potatoes and cut into large chunks. Toss with pepper, the remaining pesto, and ½ teaspoon salt. Sprinkle the chicken with pine nuts and raisins. Serve with potatoes.