If using chicken breasts, butterfly them; if using thighs, leave whole. Pat the chicken dry and season all over with salt and pepper.
Heat the olive oil in a large Dutch oven over medium heat. Working in batches if needed, brown the chicken until golden and cooked through, about 5–7 minutes per side; the internal temperature should reach 165°F. Transfer the chicken to a plate.
Keep the pot over medium heat and add the diced onion. Cook until softened, about 5 minutes, then add the minced garlic, dried thyme, and Italian seasoning and cook 1 minute more.
Sprinkle the flour over the onion mixture and stir to coat; cook about 1 minute. Gradually add the chicken stock and Dijon mustard, stirring and scraping up any browned bits. Bring to a simmer.
Add the dry orzo, heavy cream, grated Parmesan, lemon juice, lemon zest, and the halved tomatoes (if using). Season with a heavy pinch of salt and some pepper, stir to combine, then reduce heat to low.
Cover and simmer gently, stirring occasionally, until the orzo is tender and most liquid is absorbed, about 8–10 minutes.
Taste and adjust seasoning with additional salt and pepper if needed. Stir in the baby spinach until wilted.
Return the chicken to the pot, nestling it into the orzo; allow it to warm through for a few minutes before serving.