Place the halved baby red potatoes in a saucepan, fill with water to cover the potatoes by about an inch, and add 1 teaspoon of salt. Bring to a boil and simmer for about 12 minutes until tender. Drain and set aside.

In a large skillet, heat 1 tablespoon olive oil over medium-high heat. Cut the chicken breasts in half to about ¾-inch thickness, seasoning both sides generously with kosher salt, black pepper, and paprika. Cook the chicken with sprigs of thyme for about 6 minutes until browned. Flip and reduce heat to medium, cooking for another 7 minutes until fully cooked (165°F internal temperature). Remove and let rest.

Using the same pan, heat the remaining 1 tablespoon of olive oil over medium-high heat. Add the drained potatoes cut-side down, quartered mushrooms, and 1 tablespoon chopped thyme. Cook for about 3 minutes.

In a small bowl, whisk together the whole milk and flour until well combined. Add the mixture to the pan with the vegetables, along with ½ teaspoon salt, ¼ teaspoon black pepper, and chicken stock. Simmer over medium-high heat for about 1 minute, whisking continuously until the sauce thickens.

Add the lemon zest, lemon slices, and green beans to the sauce. Simmer for another minute. Return the chicken to the pan, cover, reduce heat to medium-low, and simmer for an additional 3 minutes until the beans are crisp-tender. Finish by sprinkling with chopped parsley before serving.