Rinse 1 pound dried navy beans and remove and discard split, broken, or discolored beans. Place the beans and 4 cups hot water in a large, heavy pot or Dutch oven. Bring to a boil over medium-high heat. Boil for 2 minutes, then remove the pot from heat. Cover and let soak for 1 hour.

Meanwhile, finely chop 1 medium yellow onion (1 ½ to 2 cups), 1 large carrot (½ cup), and 1 medium celery stalk (½ cup). Finely chop 2 garlic cloves. Dice 8 ounces thick-cut cooked ham (1 cup).

When the beans are done soaking, pour through a colander to drain. Wipe the pot clean.

Heat 2 tablespoons olive oil in the same pot over medium heat until shimmering. Add the onion, carrot, and celery, and cook, stirring occasionally, until fragrant and begin to soften, about 3 minutes. Add the ham, garlic, 2 bay leaves, 2 teaspoons black pepper, 1 teaspoon kosher salt, ½ teaspoon dried thyme, and ½ teaspoon dried rosemary. Sauté until fragrant, about 1 minute.

Add the beans and stir to combine. If desired, nestle 1 smoked ham hock into the bean mixture. Add 6 cups low-sodium chicken broth and bring to a boil over high heat. Reduce the heat to medium-low and simmer gently, stirring occasionally, until the beans are tender, 1 hour 30 minutes to 1 hour 45 minutes.

Remove the ham hock. Add 2 tablespoons unsalted butter and stir until melted. Taste and season with more kosher salt as needed.