Preheat the oven to 300°F. Place a large pot or Dutch oven on medium-high heat and add the butter. Heavily salt the chuck roast on all sides (approximately 2 teaspoons) and add it to the melted butter. Allow the roast to brown, turning occasionally, for about 3 to 4 minutes on each side. Add 2 cups beef broth and bring to a simmer. Put the top on the pot and place in the oven. Cook for 4 hours or until fully tender. Remove the beef from the pot, but leave the sauce in and add the broccoli to it. Cook covered in the oven for 5 minutes. When finished, remove the broccoli from the pot and set aside with the beef to cool. The broccoli should be cooked enough to eat, but still very crunchy.
Add the remaining beef stock to the pot. Place the pot back on the stove on medium-high heat until it comes to a boil. Add the rice and at least 1 teaspoon salt and cook according to package time (the final amount of salt will depend on your preference and the saltiness of the broth). While the rice is cooking, shred the beef into small pieces.
Combine the lemon juice, soy sauce, Parmesan, mayonnaise, and remaining teaspoon of salt. Combine the sauce, beef, and broccoli with the rice.
If You Are Eating Now: Put everything back in the oven for 5 minutes. Serve hot.
If You Are Freezing for Later: Allow the beef and broccoli to cool completely. Split into individual portions. Make sure the beef is truly shredded and the broccoli is cut small, otherwise it won't unfreeze as uniformly. Freeze in freezer containers or resealable freezer bags. When ready to eat, you can reheat in either the microwave or the oven. In the oven, cook at 400°F for at least 15 minutes per portion, making sure to stir every 5 minutes. In the microwave, cook for 1 or 2 minutes at a time, stirring in between.
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