Heat the bacon grease (or butter or oil) in a heavy pot (preferably a Dutch oven) over medium-high heat. Add the onion, celery, carrot, garlic, jalapeno, bay leaves, salt, pepper, and cayenne and cook, stirring until the veggies have softened, about 10 minutes.
Add the ham, mustard, and rosemary, cook for 3 minutes more, stirring occasionally.
Remove any beans from the pot that have floated to the top. Drain and pick over any skins that have come loose. Add the beans to the sautéed vegetables along with the chicken stock. Bring to a boil, then reduce the heat to low and cook the stew at a simmer for 1 hour.
Add the kale and cook for 30 minutes more.
Turn off the heat and let sit for 15 minutes, discard the bay leaves.
You can serve the soup as is at this point, but, to make it creamier...puree 2 cups of the stew in a food processor or blender and return to the stew. Stir until fully incorporated.
Taste for more seasonings, adding more salt and pepper if desired.