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. Add the chicken in batches if needed and brown until golden and cooked through, about 5–7 minutes per side (internal temperature 165°F). Transfer the cooked chicken to a plate.
Keep the pot over medium heat and add the diced onion. Cook until softened, about 5 minutes. 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, cooking about 1 minute. Gradually add the chicken stock and Dijon mustard while scraping up any browned bits; bring to a simmer.
Stir in the dry orzo, heavy cream, grated Parmesan, lemon juice, lemon zest, and halved tomatoes (if using). Season with a generous pinch of salt and some black pepper. Reduce heat to low, cover, and simmer for 8–10 minutes, stirring occasionally, until the orzo is tender.
Taste and adjust seasoning with salt and pepper as needed. Stir in the baby spinach until wilted, then nestle the chicken back into the pot to warm through.
Serve hot with extra Parmesan and a squeeze of lemon if desired.