Add the avocado oil to a large dutch oven over medium heat.Add the onion and carrots, and saute for 3-4 minutes until the onions have softened.
Add the butter to the dutch oven and stir until melted. Whisk in the flour to create a roux. *Cook for 1 minute while whisking continuously.
Slowly whisk in the chicken broth, followed by the half and half. Cook for 2-1-2 minutes, whisking until everything is combined. Season with sea salt, paprika, and garlic powder.
Add in the frozen broccoli florets. Reduce the heat to medium-low and simmer for 12-15 minutes or until the broccoli and carrots are fork-tender.
Use an immersion blender to blend the soup a few times, making sure not to over-blend (soup should still have a slightly chunky texture).
Next, add the grated cheese and stir until it has fully melted. Ladle into bowls and serve!