Heat a small skillet over medium heat. Add pine nuts and cook, stirring frequently, until lightly browned and toasted, about 3 minutes. Cool.
In blender, combine pine nuts, basil, Parmesan, garlic, salt, and pepper. With machine running, add the oil through the top in a thin, steady stream until mixture is smooth. Transfer pesto to large bowl.
Bring a large pot of water with salt to boil. Add potatoes; cover and return water to boil. Uncover and cook until the potatoes are barely tender, about 4 minutes. Drain in colander.
Toss potatoes with pesto. Layer half the potatoes in baking dish; sprinkle evenly with half the cheddar and basil. Repeat with remaining potatoes, cheddar, and basil. Pour hot broth evenly over top. Cover tightly with foil and bake 30 minutes.
Uncover and bake until the cheese is bubbling and starting to brown, about 15 minutes. Sprinkle top with parsley.