Add the potatoes, onion, celery, garlic, chicken broth, thyme, parsley, onion powder, salt, and pepper to the slow cooker.
Cover and cook on Low for 6 to 7 hours or High for 3 to 4 hours, until the potatoes are tender.
Stir in the chopped broccoli.
Cover and cook for another 30 to 40 minutes until the broccoli is tender.
Mix the cornstarch with the cold water until smooth.
Stir the cornstarch slurry into the soup.
Add the heavy cream and shredded cheddar cheese.
Stir until the cheese has melted completely.
Mash a few potatoes with a potato masher for a thicker, creamier soup, leaving plenty of chunks for texture.
Taste and adjust the seasoning before serving.
Garnish with fresh parsley and extra shredded cheddar cheese.