Place the oil in a large pot over medium heat. Once hot, add in the carrots and onions and cook, stirring frequently, until onion is translucent...about 3-5 minutes. Add the garlic and cook a minute or so more, until fragrant. Then add in the butter and let it melt down.

Gradually whisk in the flour in small batches. Whisk constantly until all the flour is added and incorporated. Mixture will be very thick. Allow the mix to cook for 1 minute, continuing to whisk.

Whisk in the broth in small amounts, whisking constantly, until fully incorporated. Once all the broth is added, whisk in the milk and increase heat to med-high. Let this mixture come to a low boil.

Once it reaches a boil, stir in the broccoli and lower the heat to med-low. Allow to simmer until the broccoli is tender...about 7-9 minutes. (If using larger sized florets, it may take longer). Then stir in the cream cheese and let that melt down into the soup.

Stir in the seasonings and taste to see if you think it needs anything else. Then, if you'd like a less chunky soup, use an immersion blender to puree to the desired consistency. You could also use a blender or food processor in small batches, just be careful not to burn yourself.

Remove the pan from the heat. Stir in both of the shredded cheeses until it is all melted and incorporated in. That's it, you're ready to serve!