Boil the potatoes in vegetable broth for about 20 minutes.
Meanwhile, steam the green beans in a vegetable steamer basket in a separate pot.
Drain the potatoes, but catch the vegetable broth in a measuring cup. Use a potato masher and mash the potatoes, then use an electric mixer and add parts of the saved vegetable broth until the mashed potatoes have the desired consistency. You can also add a splash of half and half, if you want to add a little creaminess.
Fold in the green beans and pancetta.