Bring a pot of water to boil over the stove. Add green beans and boil for about 3-5 minutes, or until just fork tender. Remove beans with a slotted spoon and immerse in an ice bath to stop the cooking and preserve color.
Add potatoes to the bean water (or refresh if you like), and boil for about 10-15 minutes, or until just cooked through (be very careful not to overcook). Drain and rinse with cold water to help stop the cooking.
Slice cooked potatoes into 1/4-1/2 inch coins and add to a large bowl and add the beans. Add pesto and toss gently to combine. Taste, and add additional salt and pepper as necessary. Add pine nuts just prior to serving.