Heat the olive oil in a large Dutch oven or soup pot over medium-high heat. Season the whole chicken thighs with about ½ teaspoon salt and ¼ teaspoon black pepper.

Add the chicken thighs to the hot pot and cook for 3–4 minutes per side, until lightly browned. The chicken does not need to be cooked through at this point. Transfer it to a clean plate and set aside.

Reduce the heat to medium. Add the onion and carrots to the same pot. Cook for 4–5 minutes, stirring occasionally and scraping up the browned bits from the bottom of the pot.

Add the garlic, thyme, and rosemary. Cook for about 30 seconds, stirring constantly, until fragrant.

Add the potatoes, chicken broth, Dijon mustard, remaining salt, and pepper. Return the chicken thighs and any accumulated juices to the pot.

Bring the soup to a boil, then reduce the heat to maintain a gentle simmer. Partially cover and cook for 15–20 minutes, or until the potatoes are fork-tender and the chicken has reached an internal temperature of 165°F.

Transfer the chicken thighs to a cutting board or bowl. Shred the chicken using two forks, then set it aside.

Use a potato masher or the back of a wooden spoon to lightly mash about ¾ cup of the potatoes directly in the pot. Leave the remaining potatoes chunky. This naturally thickens the broth while keeping plenty of texture.

Stir in the chopped kale and simmer for 3–4 minutes, or until tender.

Reduce the heat to low. Return the shredded chicken to the pot and stir in the half-and-half. Cook gently for 1–2 minutes, just until everything is heated through. Do not let the soup boil after adding the half-and-half.

Remove from the heat and stir in the fresh lemon juice. Taste and add additional salt, pepper, Dijon, or lemon juice as needed. Let the soup rest for about 5 minutes before serving to allow the broth to thicken slightly.