Preheat the oven to 350°F. Lightly grease a 9x9-inch baking dish.
Cook the pasta according to the package directions until just tender. Drain and set aside.
Melt 2 tablespoons of butter in a large skillet over medium heat.
Add the diced onion and cook for about 4 minutes, stirring occasionally.
Add the minced garlic and fresh thyme. Cook for another 2 minutes, stirring often.
Sprinkle the flour over the onion mixture and stir until everything is well combined.
Slowly whisk in the chicken broth and heavy cream.
Bring the sauce to a gentle simmer and cook, stirring often, until it thickens to about the consistency of gravy or condensed soup.
Add the cooked pasta, shredded rotisserie chicken, and frozen mixed vegetables to the sauce. Stir until everything is evenly coated.
Transfer the mixture to the prepared 9x9-inch baking dish.
Melt the remaining 1 tablespoon of butter in a small bowl. Crush the Ritz crackers into the melted butter and stir until the crumbs are coated.
Sprinkle the buttery cracker mixture evenly over the casserole.
Bake for 20-25 minutes, until hot and bubbly.
Turn the oven to broil and broil for a few minutes, watching closely, until the cracker topping is golden brown.
Let the casserole rest for about 5 minutes before serving.