In a large pot, melt butter over medium heat and saute the chopped onions and garlic for about 5 minutes, until translucent.
Add the chopped celery, and a splash of water to keep everything moving. (Using water during the cooking process is a great way to keep the fat content low, without needing to add any extra oil or butter!)
While the onions and celery are cooking (about 5 more minutes) shred the carrots, along with any broccoli stems that might otherwise be wasted.
Add the shredded carrots and broccoli stems into the pot, along with the broccoli florets, adding just enough water to cover. (about 3-4 cups)
Bring the water to a boil, then cover and reduce heat to simmer for 30 minutes.
Once the veggies are nice and tender, transfer the soup in batches to a blender or food processor. (If you're using a blender, make sure your batches are small and BE CAREFUL! Hot soups tend to create a LOT of pressure while blending, so hold the top down tight!)
Once it's all blended, return the pureed soup to the stove to keep warm, and add the nutmeg and sea salt, to taste. (I started with 1 teaspoon of Himalayan salt)
Finally, add the shredded goat cheddar, and stir until well melted.
Adjust seasonings to taste, then serve piping hot!