Trim excess fat from the pork shoulder and cut it into 2-inch chunks. This helps it cook evenly and absorb flavors beautifully.
Chop the carrots into 1-inch thick rounds, and dice the large yellow onion into uniform pieces. Mince the garlic cloves finely to release maximum flavor.
In a skillet over medium heat, add a splash of oil and sear the pork chunks until they develop a golden-brown crust on all sides, about 5-7 minutes. This step locks in juices and adds depth to the flavor.
Transfer the seared pork to the slow cooker. Pour in the broth, ensuring it covers at least halfway up the meat.
Add the chopped carrots, diced onions, bay leaves, and a sprig of thyme to the slow cooker. Gently stir everything together to combine the flavors.
Cover the slow cooker and cook on low for about 8 hours. The house will be filled with a savory aroma as the pork becomes tender and the vegetables soften.
After cooking, check that the pork is easily shreddable with a fork and the vegetables are tender. Remove the bay leaves and thyme sprig.
If you'd like a thicker stew, mash the potatoes and stir them into the broth. Let it cook uncovered for 15 minutes to thicken, or stir in a slurry of cornstarch and water and cook for a few more minutes until bubbly.
Taste the broth and adjust seasoning with additional salt and pepper if needed. Let the stew rest for 10 minutes to allow flavors to meld.
Serve the hearty stew hot in bowls, with crusty bread or over rice. The pork should be fall-apart tender, and the broth rich and flavorful, inviting comfort with each spoonful.