1-First Step: Prep and mise en place Wash and peel the potatoes if you prefer them without skins, then dice into 1/2 to 1-inch pieces for even cooking. Peel and dice the carrots, chop the celery ribs, and dice the white onion. Mince the parsley and measure the broths, milk, butter, and flour so everything is ready when you need it. Having the diced cooked ham ready will speed things up.

2-Second Step: Sauté the aromatics Heat 2 tablespoons olive oil in a stock pot over medium heat. Add the diced carrots, celery, and white onion. Cook, stirring often, until the vegetables are slightly softened and the onions look glossy, about 5 minutes. This builds a flavorful base without browning.

3-Third Step: Add potatoes, broth, and ham Add the diced potatoes, 6 cups vegetable broth (or chicken broth, or the bouillon option), and 2 cups cooked diced ham to the pot. Bring to a boil over medium-high heat, then reduce the heat to medium and simmer until the potatoes are tender, about 15 minutes. Stir in 1 teaspoon freshly cracked black pepper while the soup simmers.

4-Fourth Step: Make the milk-roux While the soup simmers, warm a separate saucepan over medium-low heat. Melt 2 tablespoons salted butter, then whisk in ¼ cup all-purpose flour until smooth. Cook the mixture for 1 minute to form a blonde roux; this removes any raw flour taste and helps thicken gently. Gradually whisk in 2 cups milk, a little at a time, breaking up lumps so the sauce stays smooth. Cook, whisking frequently, until the mixture thickens and is warmed through, about 4 minutes. Keep the heat moderate so milk does not scorch.

5-Fifth Step: Combine and finish cooking Carefully pour the milk-roux mixture into the stock pot with the simmering vegetables and ham. Whisk briefly to combine. Continue to cook over medium heat until the soup thickens and the vegetables are tender, about 8 to 10 minutes. Taste and add salt if needed, remembering ham adds saltiness. Stir in 2 tablespoons minced fresh parsley just before serving.

6-Final Step: Serve and garnish Ladle soup into bowls and finish with an extra sprinkle of parsley and a crack of black pepper. Serve with crusty bread or a light side salad for a full meal. For a simple dessert pairing, try a bright berry trifle or a slice of fruit pizza to keep things fresh and family-friendly.