Heat 1 tablespoon of olive oil in a large Dutch oven over medium heat. Add the chicken and cook about 2 minutes per side. Remove and set aside. Add in 1 tablespoon of butter. Once melted, add the carrots and onions and cook for about 8 minutes, stirring often, until just starting to soften.

Add the remaining 2 tablespoons of butter and the garlic and cook until the butter has melted. Sprinkle the flour over the top and stir to fully saturate the flour. Slowly add in the chicken broth, stirring constantly. Return the chicken breast to the pot, reduce the heat to low, and cover. Cook for about ten minutes, or until the chicken is just cooked through. Remove from the pot and place on a cutting board until slightly cooled.

Meanwhile, return the heat to medium. Add the almond milk, mustards, and cheeses and cook, stirring often until the cheese is melted.

When the chicken is cool enough to handle, shred with your hands or two forks. Return to the pot with the ham and cook, stirring often, until heated through. Season to taste with salt and pepper.

Dish into bowls and garnish with fresh thyme leaves. Enjoy!