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Step 1
Heat the butter in a large Dutch oven or soup pot over medium heat. Add the onion and salt and cook, stirring frequently, until softened, 4 to 5 minutes. Add the garlic and cook until fragrant, about 30 seconds. Do not brown.
Step 2
Add the broth, water, ham steak, bacon, peas, thyme sprigs, and bay leaves. Increase the heat to high and bring to a boil, stirring frequently to keep the peas from sticking to the bottom of the pot. Reduce the heat to low, cover, and simmer until the peas are tender but not falling apart, about 45 minutes.
Step 3
Remove the ham steak and place it on a plate; cover with foil and set aside. Stir in the carrots and celery and continue to simmer, covered, until the vegetables are tender and the peas have almost completely broken down, about 30 minutes longer.
Step 4
Meanwhile, shred the ham steak into small bite-size pieces with two forks. Cover with foil again.
Step 5
Remove and discard the thyme sprigs, bay leaves, and bacon slices. Add the shredded ham to the soup and return to a simmer. Add a few grinds of pepper, then taste and adjust seasoning if necessary (depending on the saltiness of the ham and bacon you used, you may need an additional 1/4-1/2 teaspoon salt). Ladle the soup into bowls and top with fresh croutons, if using. (The soup will thicken as it sits on the stove; thin it with water and adjust seasoning as necessary.)
Step 6
Note: A ham steak is a thick slice of cooked ham cut from a whole ham roast. They can be found packaged in the refrigerated meat section of the supermarket, near the bacon.
Step 7
Note: Regular sliced bacon can be used, but the thinner slices are a little harder to remove from the soup.
Step 8
To Make Fresh Croutons: Melt 2 tablespoons of unsalted butter in a medium skillet over medium heat. Add 2 cups of cubed good-quality French or Italian bread and cook, stirring frequently, until golden brown and toasted, 3 to 5 minutes.
Step 9
Make-Ahead/Freezer-Friendly Instructions: The soup can be made up to 3 days ahead of time and refrigerated, or frozen for up to 3 months. Defrost the soup in the refrigerator for 12 hours and then reheat it on the stovetop over medium heat until hot. The soup will thicken once cool, so thin with water and adjust seasoning as necessary.