Step 1: Sauté the Aromatics
In a large pot or Dutch oven, heat the butter and olive oil over medium heat. Add the chopped onions and sauté for 5-7 minutes until they’re soft, fragrant, and just beginning to turn golden. Add the minced garlic and cook for another 1-2 minutes, stirring constantly to prevent burning.

Step 2: Make the Roux
Sprinkle the flour over the sautéed onions and garlic. Stir continuously for 2-3 minutes to form a roux — this helps thicken the soup. It should look like a smooth, paste-like mixture without lumps.

Step 3: Add the Liquid
Gradually pour in the chicken broth, whisking constantly to incorporate the roux into the liquid without clumps. Bring the mixture to a gentle simmer and let it cook for 5-10 minutes to thicken slightly.

Step 4: Add the Protein and Flavor
Add the cooked chicken and diced ham to the pot. Stir in the Dijon mustard, smoked paprika, salt, and pepper. Reduce heat to low and let everything simmer together for 10 minutes, allowing the flavors to meld.

Step 5: Finish with Cream and Cheese
Slowly stir in the half-and-half and shredded Swiss cheese. Keep the heat low to prevent curdling. Stir until the cheese is fully melted and the soup is silky smooth. If using peas, corn, or diced potatoes, add them now and simmer until they’re tender. Garnish with chopped parsley before serving.