In a large pot, bring salted water to a boil. Add the halved baby potatoes and cook until tender, about 15-20 minutes. Drain and let cool slightly.

While the potatoes are cooling, prepare the arugula pesto. In a food processor, combine the arugula, Parmesan cheese, pine nuts, garlic, lemon juice, and a pinch of salt and pepper. Pulse until finely chopped.

With the food processor running, slowly drizzle in the olive oil until the mixture is smooth and creamy. Taste and adjust seasoning if necessary.

In a large mixing bowl, combine the cooled potatoes with the arugula pesto. Toss gently to coat the potatoes evenly.

Transfer the potato salad to a serving dish and garnish with cherry tomatoes and sliced green onions. Serve warm or at room temperature.