Melt butter over medium heat in a large skillet. Add onion and cook until soft and translucent, 3 to 4 minutes. Add garlic and cook until fragrant, about 30 seconds.
Add Dijon mustard and orzo. Cook, stirring, until orzo is lightly toasted. Sprinkle in flour, and stir constantly until lightly golden, 1 to 2 minutes.
Slowly whisk in chicken bone broth. Add milk and bring to a gentle simmer; sauce should begin to thicken. Stir in chicken, frozen vegetables, thyme, rosemary, paprika, and poultry seasoning. Season to taste with salt and pepper.
Continue cooking until orzo is tender and sauce is thick and creamy, 5 to 8 minutes. Add a sprig of fresh thyme for garnish.