Set your Instant Pot to the sauté function. Once hot, add the olive oil, diced onion, and minced garlic. Sauté for 3-4 minutes until the onion is soft and translucent.
Add the broccoli florets to the pot and stir for another 1-2 minutes.
Pour in the broth, ensuring the broccoli is submerged. Season with salt, black pepper, and paprika if using. Close the lid tightly and ensure the vent is set to sealing.
Set the Instant Pot to high pressure and cook for 5 minutes. Once the cooking time is complete, carefully perform a quick release.
Once the steam has fully released, open the lid and stir in the heavy cream and shredded cheddar cheese until melted and combined.
If you prefer a smoother texture, use an immersion blender to puree the soup to your desired consistency.
Taste and adjust seasoning as necessary. Add lemon juice if desired for brightness.
Serve hot, garnished with extra cheese or croutons if you wish.