Place broccoli, shredded carrots and onions in slow cooker. Add salt, pepper and chicken stock. Stir well and set on high for 2 hours.
After 2 hours, remove lid and stir everything.
(Optional step) If you want, use an immersion blender and give it a puree for about 30 seconds.
Slowly add small amounts of cheese and blend until melted. Do about 1/2 cup at a time so that it melts into the soup evenly. Adding large amounts at once can cause clumping and not melt properly.
After all the cheese is melted in, leave in slow cooker on low for about 15 more minutes. Then, remove lid, stir in half and half, and you’re now ready to serve.