In the pot of an electric pressure cooker, heat the oil. Add the celery, carrots, and onion, and saute until the onions go clear, about 7 minutes. Alternatively, you can do this in a pot on the stovetop over medium heat.
Add the chicken broth and broccoli. If you are using the pressure cooker, attach the lid and turn on the pressure valve. Turn the machine on and set it to manual for 4 minutes. If you are cooking this on the stove, bring the pot to a simmer and cook until the vegetables are tender, about 20 minutes.
While the veggies are cooking, prepare the cheese sauce. In a medium saucepan on the stove, melt the butter. Add the flour, and cook, whisking for two minutes. Slowly whisk in the milk, stirring to combine. Allow the mixture to simmer, stirring, until slightly thickened. Whisk in the cheeses.
When the vegetables are done cooking, blend them slightly with an immersion blender. It's best to leave some chunks, but go with the texture you prefer.
Stir the cheese sauce into the vegetable mixture. Season to taste with salt and pepper. Serve hot.
Note: Store any leftover soup in the refrigerator in an airtight container for up to 4 days. Once the soup has chilled completely, you can freeze it for longer storage.