Spread dried pinto beans (1 pound) out in a flat layer and remove then discard split, broken, discolored beans, or small rocks. Place beans in a colander and rinse well. Transfer beans to a large bowl, and cover beans by 2 inches with water. Soak overnight.
Heat 2 tablespoons olive oil in the heavy bottom pot or Dutch oven over medium heat until shimmering. Add the onion (1 1/2 cups), carrot, celery, and jalapeño, sautéing and stirring occasionally, until onion is translucent, about 7-9 minutes.
Sit in 1/4 cup garlic and continue to sauté, stirring constantly, until fragrant, about a minute or more.
Score a large X on ham hocks (4). Nestle them into vegetables. Pour 8 cups of water over the ham hocks and vegetables. Bring to a boil, reduce heat immediately, and simmer, uncovered for 1 hour.
Add drained beans, Cajun seasoning (1 teaspoon), and bay leaves (2) to ham hocks and broth. Bring to a boil, then immediately reduce heat and continue to simmer until beans are tender, about 2 hours.
When the beans are about done, brown the sliced sausage (20 ounces), over medium heat, in a skillet on both sides. Transfer sausage to a paper towel-lined plate and dab off excess fat. Transfer sausage to soup pot.
Remove the ham hocks and cut off the meat, being careful to check for small bone fragments. Discard bones. Return ham meat to soup pot. Remove and discard bay leaves.
Using a potato masher, mash some of the beans against the side of the pot until you reach the desired thickness of the soup. Taste and adjust the seasoning to your taste.
Ladle soup into individual bowls and serve!