Season the chicken with ¾ tsp salt and ½ tsp pepper. Melt the butter in a heavy 5- to 6-quart Dutch oven over medium heat. Brown the chicken in batches for 4–5 minutes per side, until it reaches 165°F (74°C). Transfer to a plate.
Cook the shallots in the same pot for 3–5 minutes. Add the garlic, thyme, and rosemary and cook for 1 minute. Whisk in the flour and cook for another minute, until lightly browned.
Gradually stir in the stock and Dijon, scraping the bottom of the pot. Add the orzo and season the liquid with additional salt and pepper as needed. Bring to a boil, then reduce to a gentle simmer.
Simmer uncovered for 10–15 minutes, stirring every 1–2 minutes, until the orzo is tender with slight resistance and the liquid forms a creamy sauce.
Stir in the kale, Parmesan, heavy cream, lemon juice, and zest. Cook for approximately 3 minutes, until the kale is wilted. Return the chicken and collected juices to the pot and serve immediately.