Add the potatoes, broth, and 3/4 teaspoon salt, and stir to combine. Cook, covered, over low heat. The broth should simmer gently; do not boil, stirring occasionally, until the potatoes fall apart easily when poked with a fork and all the liquid has been absorbed, 25 to 30 minutes. If the liquid does not gently simmer after a few minutes, increase the heat to medium-low. Remove the pan from the heat; remove the lid and allow the steam to escape for 2 minutes.