Season chicken with 3/4 teaspoon salt and 1/2 teaspoon pepper.
Melt butter in a Dutch oven over medium heat. Working in batches, add chicken to the Dutch oven in a single layer and cook until golden brown and cooked through, reaching an internal temperature of 165 degrees F, about 4-5 minutes per side; set aside.
Add mushrooms and shallots, and cook, stirring occasionally, until tender, about 3-5 minutes. Stir in garlic and thyme until fragrant, about 1 minute.
Whisk in flour until lightly browned, about 1 minute.
Stir in chicken stock and Dijon, scraping any browned bits from the bottom of the Dutch oven. Stir in orzo; season with salt and pepper, to taste.
Bring to a boil; reduce heat and simmer, stirring occasionally, until pasta is cooked through, about 6 minutes. Stir in spinach, Parmesan and heavy cream until the spinach has wilted, about 3 minutes. Return chicken to the Dutch oven.