Preheat oven to 350 degrees and spray a 9×13-inch casserole dish with nonstick spray.
Wash, peel, and slice carrots. Slice the carrots into bite-size pieces so they will take less time to steam and cook.
In a large pot, add about two inches of water and the sliced carrots. Steam the carrot until they are fork-tender but not mushy (about 8 – 10 minutes). You want them to still have a little crunch to them. The oven will finish cooking them to perfection. Drain carrots and set aside.
While the carrots are steaming, heat a skillet over medium heat. Melt the butter and add the onions. Cook the onions until soft. Add the salt, pepper, dry mustard, and nutmeg; mix.
Add the flour and mix to make a paste. Cook for about a minute.
Slowly add the milk to the skillet, whisking continually until all the milk has been added. This is the roux for the cheese sauce and it will be thin at first but as it cooks, it thickens nicely. Be sure NOT to dump all the milk in at once. This will result in a very lumpy sauce.
Cook the sauce over medium heat for about five minutes, or until thickened. Turn off the heat and add the cheese. Stir until completely melted into the sauce.
Place carrots in the bottom of the baking dish. Pour the sauce evenly over the carrots.
Sprinkle the crushed cracker crumbs over the casserole and bake for 25 minutes, or until hot and bubbly. The top will be golden brown.