In a large saucepan, heat extra virgin olive oil over medium-high heat.
Add onion, carrot and celery, cook for 5-7 minutes while stirring often. All celery and onion to soften.
Add potato and garlic, cook for an additional 2 minutes while stirring.
Stir in flour, dry mustard and cayenne, cook, stirring often for 2-3 minutes.
Now, add broth and broccoli stems and bring everything to a boil.
Cover and reduce heat to medium. Simmer and stir occasionally for 10-12 minutes.
Stir in florets. Cover and simmer until the broccoli is tender. About 10-12 minutes.
Transfer 2 cups cooked chowder to a large mixing bowl and mash ingredients, return to pan.
Stir in cheddar and sour cream. Cook over medium heat. Stir until cheese melts and chowder is heated through. About 2-3 minutes.
Season with salt.
Serve hot.