Heat your olive oil in a large skillet over medium-high heat for about 2 minutes. Pat your beef chuck roast dry with paper towels — this makes a huge difference for getting a good sear. Place it in the hot pan and sear for 3-4 minutes per side until you get golden brown edges. Don't panic if it sticks a tiny bit; that's actually good (it means flavor).
Transfer your seared roast to the slow cooker insert. Sprinkle the minced garlic, thyme, and rosemary directly over the top. Add your bay leaves right there too. This is when the kitchen starts smelling incredible, and your family will start asking when dinner's ready.
In a small bowl, whisk together your beef broth and tomato paste until smooth. Stir it really well so no lumps hang around. Pour this mixture over your roast, making sure the liquid comes halfway up the sides (not fully covering it).
Add your onion chunks and carrot pieces around the roast. Nestle them in so they're surrounded by liquid. Don't worry about arranging them perfectly — they'll cook either way. The veggies need about 7 hours to get tender, which is why we add them now instead of later.
Cover your slow cooker and set it to low heat for 8 hours. This is the magic number for beef chuck — any longer and it gets kinda mushy, any shorter and it fights your fork. I set mine in the morning before work and come home to dinner basically done.
After 8 hours, carefully open the lid (there's steam, so watch your face). Your slow cooker pot roast should shred easily with a fork, and the veggies should be fall-apart tender. If the liquid looks too thin, you can skim off extra fat now, but honestly, I usually leave it.
Let everything rest in the pot for 10 minutes before serving. This keeps the meat juicy instead of dry. Use a slotted spoon to pull out your roast and veggies onto serving plates, then ladle that amazing gravy over everything. Everyone gets meat, veggies, and sauce — literally no extra work.