In a saucepan, heat up the olive oil. Whisk in the flour a little at a time and mix well until it starts to bubble a bit.
Slowly whisk in the chicken/vegetable broth, and then remove from heat.
Pour the mixture into your slow cooker (I use a Crock Pot), and add the chopped broccoli. Cook on low for 4-6 hours, or until the broccoli is completely cooked. Stir in the cheese 1 cup at a time, allowing it to melt completely before adding the other cup.