In a large stock pot, melt butter over medium heat.
Saute onion in butter until onions are translucent, about 3-4 minutes.
Stir in chicken broth, half and half, broccoli, baby carrots, and celery. Bring to a boil, then reduce heat and simmer for 10-15 minutes or until broccoli is soft and tender.
In a small bowl, whisk together milk and cornstarch. Pour this mixture into the soup pot and stir until soup starts to thicken (3-4 minutes).
Stir in pepper, garlic powder, thyme, nutmeg, and sea salt.
Drop the heat to low and stir in cubed Velveeta and sharp cheddar cheese.
Continue stirring until all of the cheese has melted.
Top each bowl of soup with a little extra shredded cheddar cheese and serve immediately.
