Melt the butter in a large stockpot or Dutch oven over medium heat.
Add the chopped onions and minced garlic, sautéing until the onions are soft and translucent, about 3-4 minutes.
Pour in the vegetable broth and add the frozen broccoli. Increase the heat to high and bring the mixture to a gentle boil.
Once boiling, reduce the heat to maintain a steady simmer.
Cook for about 15 minutes, or until the broccoli is fork-tender, stirring occasionally.
Reduce the heat to the lowest setting to prevent the soup from curdling. Slowly stir in the shredded cheddar cheese and heavy cream.
Continue stirring gently until the cheese is completely melted and the soup is smooth and creamy.
Season generously with salt and pepper to your liking.
Serve immediately, garnished with an extra sprinkle of sharp cheddar cheese. Leftovers can be stored in an airtight container in the refrigerator for up to 5 days.
Don't let the soup boil after adding the dairy. High heat can cause the cream and cheese to curdle or separate.
Keep the heat on the lowest setting while melting the cheese.
Add a pinch of nutmeg or mustard powder along with the salt and pepper. These 'secret' enhance the cheesy flavor without being overpowering.