Heat the olive oil and butter in a large pot over medium heat. Add the onion and carrot and cook for about 10 minutes. Add in the flour and cook again for about 2-3 minutes, then gradually add in the milk and whisk until smooth. Add the broth, beer, broccoli, bay leaves, nutmeg, cayenne, and a large pinch each of salt and pepper if desired.
Bring to a simmer. Turn down to medium heat and cook uncovered until the broccoli is tender. Usually about 20 minutes.
Remove the soup from the stove. Remove the bay leaves and puree in a blender.
Once pureed, put the soup back on the stovetop over low heat. Stir in the cheese until melted and creamy. Add the thyme and cook another 2-3 minutes.
Taste and adjust seasonings just the way you like them. Serve into bowls and top with a little extra cheddar and fresh thyme. YUM!
