Season the beef chuck roast evenly with salt and black pepper on all sides.
Heat olive oil in a large skillet over medium-high heat. Sear the roast for 3-4 minutes on each side until browned. Remove from heat.
Place the carrots, potatoes, onion, and garlic in the bottom of the slow cooker.
Put the seared roast on top of the vegetables in the slow cooker.
Pour the beef broth over the roast and vegetables.
Cover and cook on low for 8 hours, or until the meat is tender and easily shredded with a fork.
Once cooked, remove the roast and vegetables from the slow cooker and set aside, keeping warm.
In a small bowl, mix the ranch dressing mix with the sour cream until smooth.
Pour the cooking liquid from the slow cooker into a saucepan and heat over medium heat until simmering.
Whisk the ranch and sour cream mixture into the simmering cooking liquid and cook for 2-3 minutes until heated through and slightly thickened.
Serve the pot roast and vegetables with the ranch dressing sauce drizzled on top.