Heat the olive oil and butter in a large pot over medium heat. When the oil shimmers, add the onion and carrot and cook until fragrant, about 10 minutes. Whisk in the flour and cook until golden, about 2 minutes, then gradually whisk in the milk until smooth. Add the broth, beer, broccoli, bay leaves, nutmeg, cayenne, and a large pinch each of salt and pepper. Bring to a simmer, reduce the heat to medium and cook, uncovered, until the broccoli is tender, about 20 minutes. Remove the soup from the stove. Remove the bay leaves and puree in batches in a blender or use an immersion blender. Return the soup to the stove and set over low heat. Stir in the cheese until melted and creamy. Add the thyme and cook another 2-3 minutes. Taste and adjust seasonings as desired. Laddle into bowls and top with a little extra cheddar and fresh thyme. Enjoy!