Place cut potatoes in a saucepan. Add water 1-inch above potatoes, and add 1 teaspoon salt. Bring to a boil, and simmer 12 minutes or until tender. Drain.
Heat a large skillet or pan over medium-high heat. Add 1 tablespoon oil.
Cut chicken breasts in half, about ¾-inch thick then season both sides with salt, pepper, and paprika.
Add chicken and thyme sprigs to the pan and cook for 6 minutes until browned. Flip the pieces over and reduce heat to medium. Cook for 7 minutes or until no longer pink and the internal temperature reaches 165°F.
Remove chicken from the pan and transfer to a plate to rest. Discard thyme sprigs.
Using the same pan, set over medium-high heat. Add the remaining 1 tablespoon oil.
Add potatoes cut-sides down, mushrooms, and 1 tablespoon chopped thyme. Cook 3 minutes or until browned, and then stir.
Combine milk and flour in a small bowl, stirring with a whisk.
Add flour mixture, ½ teaspoon salt, ¼ teaspoon pepper, and stock to the pan. Simmer over medium-high heat for about 1 minute, whisking sauce to thicken and remove any lumps that form.
Add lemon zest, lemon slices, and beans to the pan then let it simmer for 1 minute. Add chicken, cover and reduce heat to medium. Simmer 3 minutes or until beans are crisp-tender. Sprinkle with parsley and serve.
Notes
You can substitute cashew, almond, soy or coconut milk for the dairy if you are avoiding cow's milk. Using all chicken broth also works, it will just be less creamy.
Use gluten-free flour if you are avoiding wheat flour.
Sweet potatoes are a great substitute for red potatoes.
You can steam instead of boil the potatoes until form tender.