Rinse beans and soak overnight in a large pot filled with water. Or if you forget to soak overnight, cover the pot with a lid and bring the water to a boil for 2 minutes, then turn the burner off and soak for 1 hour before continuing. Drain the soaking liquid from the beans.
Saute the onion, jalapeno, and garlic in a little oil, just like in the Instant Pot directions, then add the drained beans. Add the broth and enough fresh water until the beans are covered by at least an inch of water.
Bring the water and beans to a boil on high heat. Once the water is boiling, cover the pot and turn the heat down to low. Simmer for 2 to 3 hours, stirring occasionally, until the beans are nice and tender. You will know they are done because they will be soft and the skin will start to split open. Be sure to check the water level every 30 minutes or so, just to make sure there is still plenty of water and add in more if needed.
Once beans are soft, drain most of the cooking liquid from the beans into a separate bowl. Don't dump it out because you will likely need to add some of it back to the beans to get them to the right consistency.
Use a potato masher or immersion blender to mash the beans until they reach the consistency you like, adding reserved cooking liquid as necessary. Taste as you go and if the beans are too salty, just add regular water instead of the cooking liquid.
Top with grated cheese and serve with your favorite Mexican entrees!