Put your left over ham bone and any scraps of meat and fat that you have into a pot. Use a pot that will allow your ham bone to be covered with water.
Add the onion, carrots, bay leaves and about a teaspoon of pepper. At this point I don't usually add salt because some hams are very salty. I wait until the very end of the cooking time to add salt if it is needed.
With the bay leaves I usually add about five small or two large. It's really up to you if you like the flavor bay leaves brings to the party then add a couple extra.
Turn the stove up to medium high and put you pot on the burner..
Pour the dried beans into a fine mesh strainer and rinse. Remove any stones and any beans that are discolored.
Once your beans are nice and clean dump them into the pot, turn the heat up to high and get it to boiling.
Bring the pot of beans and ham up to a full boil and let them boil for about thirty minutes. Turn the heat down just enough to keep a good boil going but not so much of a boil that the liquid is sputtering out of the pot all over your stove. You can put a lid on but leave a gap so some of the steam can escape.
You want some of the water to evaporate as it cooks. Stir occasionally and cook it like this for about an hour. Stir and turn the heat down so your ham and beans are at a simmer. Continue to cook it like this until your beans are tender.
You can add more pepper at this point and taste it to see if it needs any salt. By now the water has probably turned a nice creamy color from some of the beans cooking down.
Use a big spoon to scrape the tender meat from the bone into the pot.