Begin by rinsing the split peas thoroughly under cold water until the water runs clear. This helps remove dirt and excess starch, ensuring a smooth texture.
Prepare your vegetables: peel and chop the carrots into bite-sized pieces, dice the onion, and mince the garlic. Set everything aside for easy assembly.
If using a ham hock, rinse it briefly and set aside. This will add smoky richness to the soup as it cooks.
Add the rinsed split peas, chopped carrots, diced onion, minced garlic, and ham hock (if using) into the slow cooker. Pour in the vegetable broth, making sure everything is submerged.
Season the mixture with dried thyme, add the bay leaf, and sprinkle in black pepper. Cover the slow cooker with the lid.
Set the slow cooker to low and let it cook for 6 to 8 hours. During this time, the peas will soften and break down, transforming into a thick, velvety texture, while the house fills with a smoky aroma.
After cooking, carefully remove the ham hock, shred the meat, and discard the bone and bay leaf. Return the shredded meat to the soup, stirring well to combine.
Taste the soup and adjust the seasoning with more black pepper or a splash of lemon juice or vinegar for brightness. If the soup is too thick, stir in a little hot broth until it reaches your preferred consistency.
Let the soup rest for about 10 minutes to allow flavors to meld and the texture to thicken slightly. Serve hot, ideally with crusty bread on the side for a cozy, satisfying meal.