Preheat oven to 375 degrees Fahrenheit
Grease a 9 x 13 inch dish with nonstick spray.
Add the thinly peeled and sliced carrots to the baking dish and set side.
In a small medium saucepan, melt ½ cup butter over medium-height. Slowly whisk in flour to butter to make a roux. Then slowly whisk in all the milk followed by your salt, dry mustard, and black pepper. Cook mixture over medium heat until it thickens about 4-5 minutes.
Add in shredded cheese, remove from heat and stir until melted.
Pour over the top of carrots in a baking dish.
Combine the Ritz crackers and melted butter in a small dish. Evenly sprinkle over the top of the cheese sauce.
Cover the baking dish with foil and bake for 30 minutes. Remove foil and bake for another 15 minutes or until carrots are tender.
Let stand five minutes before serving to let the cheese sauce thicken.
Garnish with chopped parsley before serving if desired.