Place a large dutch oven or pot over medium high heat. Add in olive oil. Once oil is hot, add in diced chicken breast and season with salt and pepper. Cook chicken for 4-6 minutes or until cooked through and no longer pink. Remove chicken from pot and transfer to a bowl; set aside.

In the same pot, add in 1/2 tablespoon olive oil, chopped onion, sliced carrots, diced potatoes, diced cauliflower, and thyme. Sauté for a few minutes until the onion begins to soften, then add in milk, chicken broth, and salt and pepper. Allow to simmer uncovered for 10 minutes or until potatoes are fork tender.

Remove 3 cups of the mixture from the pot and add to a blender. Blend until smooth, then transfer puree back to the pot. Stir in cooked chicken and frozen peas. Allow to simmer for 5-10 more minutes to thicken. Taste and add more salt and pepper, if necessary. Garnish with extra black pepper and fresh thyme, if desired.