Bring a large pot of salted water to a boil over high heat. Add the potatoes and cook until tender, about 12-15 minutes. Drain and allow them to cool completely.
In a large bowl, combine the pesto, vinegar, and salt. Add the cooled potatoes, basil, cucumber, and eggs and toss to coat. Will keep in an airtight container refrigerated for 2 to 3 days.
