Fill a 6-8 quart stockpot with water and bring to a boil.Start by making a veloute with the butter, flour, and chicken stock. To start the roux, melt the butter and stir in the flour until well dissolved for about 2 minutes. Do not leave it alone on the stove, or your roux will burn. Instead, turn down the heat, add the chicken stock, and quickly whisk the roux and chicken stock together until the roux is fully dissolved.Turn heat back on to medium-high heat, bring the sauce to a boil while whisking, and cook for 2 minutes and then remove from heat. Add the cheese, salt, and pepper and whisk until all cheese is melted.Blanch the broccoli in a separate pot by placing the broccoli in the boiling water for about 2-3 minutes until the color of the broccoli turns bright green.Strain broccoli in a colander and cool down with cold water.Chop cooled broccoli into smaller pieces and add to the cheesy veloute sauce.Fold in the rice to the sauce.Grease a Corningware French White 2.5 qt casserole dish with butter. Once the rice mixture is cooled to room temperature, spread the mixture into the casserole dish, cover, and refrigerate until ready to heat. I usually prepare this a couple of days ahead of time before Thanksgiving.You can also vacuum seal each batch and freeze it for months of storage.When ready to heat it, remove the lid, and place it in a pre-heated oven at 350 degrees for 30 minutes until the temperature reaches 165.