Place the potatoes in a large pot of salted water and bring to a boil over high heat. Cook until tender, 15 to 20 minutes. Drain and return the potatoes to the pot.
With a potato masher, mash the cooked potatoes until more or less smooth, but still with some chunks. Stir in the olive oil. Add enough of the broth to moisten and make the potatoes a little bit creamy. Season to taste with salt and pepper and serve.