Heat oil and butter in a large nonstick pot over medium-high heat.
Add onion, garlic, celery, broccoli and saute until vegetables are partially softened and garlic is fragrant. This takes about 5 minutes.
Add broth, spinach, mustard, basil, oregano, thyme, parsley, salt, pepper and mix until combined.
Reduce heat to medium and continue cooking uncovered until all the veggies are softened.
Reduce heat to low and use a hand-held immersion blender to puree the soup until smooth and creamy. You can also puree in a blender in batches.
Mix in heavy cream slowly. I only added about ¾ cups because I added more as a topping, when serving. However, more can be added, per your preference.
Garnish with toppings of your choice and enjoy!