Start by chopping your pork shoulder into 2-inch chunks, then set them aside. Peel and chop the carrots into thick slices, and dice the onion into small pieces. Mince the garlic cloves.
In a skillet over medium-high heat, add a little oil and brown the pork chunks in batches until they develop a deep golden crust—about 3-4 minutes per batch. This step adds flavor and a rich aroma.
Transfer the browned pork to your slow cooker. Add the chopped carrots, diced onion, minced garlic, bay leaves, and thyme sprigs.
Pour in the broth and add the diced tomatoes along with soy sauce if using. Give everything a gentle stir to combine all the flavors.
Cover the slow cooker with its lid and cook on low for 6 to 8 hours. During this time, your house will fill with a savory, comforting aroma as the pork becomes irresistibly tender.
About halfway through, check the stew. If the liquid appears low, add a splash more broth to keep everything moist. Stir gently to distribute the ingredients evenly.
Once the cooking time is up, remove the bay leaves and thyme sprigs. Taste the broth and season with salt and pepper as needed.
If you prefer a slightly thicker gravy, turn the slow cooker to high and cook uncovered for an additional 10-15 minutes until the sauce has thickened and glossy.
Let the stew rest for about 10 minutes to allow the flavors to settle and the sauce to thicken further. Serve the hearty, tender pork and vegetables in bowls, garnished with fresh herbs if desired.