Heat olive oil in a saucepan over medium-low heat. Add onion and garlic; cook and stir until translucent, 10 to 15 minutes. Add broccoli stalks, potatoes, broccoli florets, and celery root; toss until coated in oil. Cover vegetables with chicken stock; bring to a boil.
Reduce heat and simmer, stirring occasionally, until vegetables are easily pierced with a fork, 20 to 25 minutes. Remove soup from heat.
Fill a blender no more than halfway with liquid and vegetables. Cover and hold lid down; pulse a few times before increasing blender to maximum speed. Puree until soup is light green and creamy, 45 seconds to 1 minute. Repeat with remaining soup, working in batches.
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