Heat 1 tablespoon of olive oil in a large pot over medium-high heat. Dab the chuck roast dry with paper towels and generously season it all over with salt and black pepper. Sear the roast in the pot until it's deeply browned on both sides, about 4–5 minutes per side. Once browned, transfer the roast to your slow cooker.
Add the remaining 1/2 tablespoon of olive oil to the same pot. Add the chopped onion and sauté for 2 minutes, then stir in the minced garlic and sauté for 30 seconds more. Pour this onion mixture over the roast in the slow cooker. Return the pot to the heat, then pour in 1 1/4 cups beef broth, the Worcestershire sauce, thyme, and rosemary. Scrape up any browned bits from the bottom with a wooden spoon—this adds a lot of flavor to the dish. Once everything is combined, remove the pot from the heat.
Layer the halved Yukon Gold potatoes and carrot chunks over the onion and roast in the slow cooker. Pour the flavored beef broth mixture evenly over the top, then season everything with additional salt and black pepper to taste. Cover and cook on low heat until the roast and vegetables are very tender, about 8 to 9 hours. I like to check the vegetables toward the end and give a gentle stir to be sure everything cooks evenly.
Once everything is tender, remove the roast and vegetables from the slow cooker. Shred the roast, discarding any excess fat, and cut the potatoes into smaller pieces if you'd like. Set aside while you prepare the gravy.
Pour the cooking broth from the slow cooker through a fine mesh strainer into a small saucepan. Heat the saucepan over medium-high heat. In a small bowl, whisk the cornstarch with 3 tablespoons of beef broth until smooth, then pour this slurry into the hot broth. Whisk constantly and bring to a simmer; cook for 30 to 60 seconds, until thickened. For extra richness, I sometimes add a splash of Worcestershire sauce at this stage.
Arrange the shredded roast and cooked vegetables on a serving platter. Pour the prepared gravy over the top and finish with a generous sprinkle of fresh parsley. Serve warm.