Prepare the Beef (Optional but Recommended): Heat olive oil in a large, heavy skillet over medium-high heat. Pat the chuck roast completely dry with paper towels. Sear the beef for 3-4 minutes on each side until a deeply browned, caramelized crust forms.
Transfer to Slow Cooker: Place the beef into the bottom of a 6-quart (or larger) slow cooker. If using potatoes, carrots, and onions, arrange them neatly around the sides of the roast.
Mix the Three Envelopes: In a medium bowl or large liquid measuring cup, combine the brown gravy mix, ranch dressing mix, and Italian dressing mix. Add the 2 cups of water (or beef broth) and whisk thoroughly until the dry ingredients are completely dissolved and the mixture is smooth.
Pour and Cook: Pour the seasoned gravy mixture evenly over the beef and vegetables.
Set It and Forget It: Place the lid securely on the slow cooker. Cook on the LOW setting for 8 to 9 hours (or on HIGH for 4 to 5 hours, though cooking on LOW is strongly recommended for the most tender, fall-apart results).
Shred and Serve: Once the cooking time is complete, the meat should be incredibly tender and easily yield to a fork. Shred the beef directly in the slow cooker to allow it to absorb the thickened gravy. Serve hot over mashed potatoes, rice, or egg noodles.