Heat the oil in a large pan over medium heat. Add onions and carrots. Cook for about 5 minutes, without browning stirring occasionally. Add salt and pepper and stir. Add the garlic and cook for one minute. Remove and put in the slow cooker.

Wash and trim broccoli. Rough chop and add to the slow cooler. Add the chicken stock and cook on low for 3-4 hours.

In a bowl add flour and milk. Whisk until incorporated and add to the slow cooker. Turn the slow cooker on high and let the contents cook for 30-45 minutes. Add cheese and let it melt. Turn off the slow cooker and remove about 1/2 cup of broccoli. Using an emulsifying blender, blend until smooth. This can also be done in batches in a blender. Chop the remaining broccoli and add to the soup.