Heat the oil in a large pot over medium heat.
Add the onion and carrot to the pot and saute for 2 to 3 minutes, or until just softened.
Stir in the garlic and allow to cook for 1 minute.
Move the vegetables to the side of the pot.
Place the butter into the cleared space and allow to melt.
Whisk the flour in with the melted butter. It’s ok if the vegetables get mixed in a little.
Let this mixture cook for 30 seconds, or until you start to see bubbles forming.
Whisk in the chicken broth, broccoli, and garlic powder.
Bring to a simmer and allow to cook for 20 minutes or until the broccoli has softened.
Stir in the heavy cream and cheese. Heat until the cheese has melted and the cream has warmed.
Season with salt and pepper to taste.
Serve topped with additional cheese if desired.