Place a large pot or dutch oven over medium heat and add 2 tablespoons of butter. Once melted, saute onion until softened.
Add the minced garlic and saute for a minute.
Add the broccoli florets and 4 cups of chicken broth. Cover it with the lid and let it simmer for about 10 minutes.
After 10 minutes, puree the soup using a handheld blender until smooth. If you don’t have one, you can use a regular blender to puree it.
Place a small saucepan over medium-high heat. Add the remaining 2 tablespoons of butter and 3 tablespoons of all-purpose flour and whisk until it starts to thicken. Add the butter-flour mixture into the soup and stir everything until well combined.
Add 3/4 cup of cream and season it with salt and pepper. Mix well. Make a taste test and adjust seasonings if needed. Serve in bowls and enjoy!