Using either the "stove-top-safe-rated" insert of your slow cooker *or* a large saute/frying pan, melt the butter over high heat. Dust one side of each chicken breast liberally with the salt and pepper. Once the butter is melted and bubbling, work in batches to place the chicken seasoned-side down and sear for 3 to 4 minutes, or until they start to form a brown crust. While cooking, season the now up-facing side and then flip over to sear for an additional 3 to 4 minutes. Transfer the now-cooked chicken to a plate and repeat for the rest of the batches (this took me about 2 batches).

Transfer the chicken to the slow cooker insert and add the onion, rinsed dulse, and either broth or water. Note: add enough broth or water until the top of the ingredients are just slightly covered.

Cook in the slow cooker for 4 hours on high or 8 hours on low.

Just before serving, pull the chicken breasts from the soup and add to a large bowl. Using either a mixer or two forks, shred the chicken into smaller strips and pieces and then return to the soup. Add the fresh lemon juice, taste and season with more salt if needed, and serve in individual bowls with the green onion.

Leftovers will keep refrigerated for up to 5 days or frozen for up to 5 months. To freeze, I recommend either freezing in one large batch or spooning into smaller serving-sized containers for freezing. To defrost, pop the frozen soup into an appropriately sized pot, cover, place over medium heat until simmering again.