In a 2–3 quart saucepan or small soup pot, melt 1 tablespoon butter over medium heat. Add the diced onion, carrot, and celery. Cook, stirring occasionally, until the onion is translucent and vegetables are softened, about 4–5 minutes. Add the minced garlic and cook 30 seconds more until fragrant.

Make roux

Push the vegetables to the side or reduce heat slightly and stir in 1 tablespoon flour. Cook the flour with the vegetables for 1 minute, stirring constantly, to remove the raw flour taste.

Add liquids and seasonings

Slowly whisk in 2 cups chicken broth until smooth. Add 1 cup whole milk, 1/2 bay leaf (or a small whole bay leaf), and 1/4 teaspoon dried thyme. Bring the mixture to a gentle simmer over medium-low heat, stirring occasionally, and let it simmer 6–8 minutes to thicken slightly and meld flavors. Season with 1/2 teaspoon salt and 1/4 teaspoon freshly ground black pepper. Taste and adjust seasoning if needed.

Ham & Pasta

Cook pasta and add ham

When the broth/milk mixture is gently simmering, add 1/2 cup elbow macaroni (uncooked). Continue to simmer uncovered, stirring occasionally so the pasta doesn't stick, until the pasta is al dente, about 8–10 minutes (check package times and taste a piece). About 3 minutes before the pasta is done, stir in 1 cup diced cooked ham so it warms through and releases flavor into the soup.

Finishing & Garnish

Finish soup

If using, stir in 1/4 cup frozen peas and cook 1–2 minutes until heated through. Remove the bay leaf. If you want a slightly richer soup, stir in 1/4 cup shredded sharp cheddar off heat until melted. Taste and adjust salt and pepper.

Serve

Ladle the soup into bowls and garnish with 1 teaspoon chopped fresh parsley if desired. Serve hot.