Cut your broccoli into bite-size florets.
Heat the oil in a heavy-bottom stockpot over medium heat. Add in the onion, carrot, garlic and sauté for about 3 minutes.
Add the flour and whisk well to combine.
Slowly add in the stock/broth whisking continuously until well incorporated.
Next, add in the milk and cream and stir to combine.
Bring the liquid to a boil, then reduce the heat to a simmer.
Add in the broccoli florets and season with sea salt and pepper to taste.
Simmer for about 15 minutes, or until the broccoli is tender, stirring occasionaly. Your soup should be nicely thickened.
Remove from the heat and garnish with chopped parsley.
Serve while hot and enjoy!