For the Sauce (I recommend making this a day ahead for best consistency) 

1. In a medium saucepan, melt the butter (or heat the oil) over medium heat. Once melted, whisk in the cornstarch or flour, garlic powder, salt, and black pepper. Stir for 2 minutes on medium-low heat until the color of roux gets slightly darker in color.
2. Gradually whisk in the coconut milk, non-dairy milk and optional bouillon, whisking constantly to remove the clumps. Cook over medium-low heat until the mixture starts to thicken or about 3 to 5 minutes. Note – If the mixture reaches a soft boil, remove from the heat, reduce heat to low, and return the pan to the stove. Continue to heat and stir until mixture has thickened.
3. Reduce the heat to low and add the shredded cheese or nutritional yeast. Gently mix with a spatula until the cheese is melted and combined. If desired, add the optional smoked paprika and any additional seasonings.

For the Instant Pot

1. Chop the broccoli floret by hand or in a food processor. Set aside. Tip: You can use just the top of the broccoli floret or chop it coarsely—whatever suits your preference!
2. Set Instant Pot to Sauté mode, manually adjust time to 2 minutes. Add the oil. Once it starts to sizzle, add the onion to the Instant Pot. Sauté for 2 minutes. Stir in the garlic and cook until fragrant, about 30 seconds to a minute. Press cancel. Add the broccoli and broth. Stir to combine. 
3. Close the lid, lock into place, flip the pressure release vent to the closed position. Cook on HIGH pressure for 1 minute. Allow a natural release.
4. Once the natural release has unlocked, remove the lid and stir in the cheese sauce, coconut milk and slurry (starch mixed with cold water). Season with salt and pepper, to taste. 
5. Mix in the optional shredded cheese then place the lid back on the pot, and keep warm for 10-15 minutes before serving. Garnish with parsley, if desired.
6. Store in the fridge for up to 3 days. 

Stovetop

1. Prepare the cheese sauce according to the recipe above. Set aside.
2. Heat oil or butter in a large, heavy-bottomed soup pot over medium-high heat.
3. Add the onion and sauté for 2 minutes until softened.
4. Stir in the garlic and cook for another 30 seconds, until fragrant.
5. Add the broccoli and broth to the pot. Stir to combine.
6. Cover the pot with a lid and simmer for 8-15 minutes, until the broccoli is tender.
7. Uncover the pot and stir in the cheese sauce, coconut milk, slurry, and salt and pepper.
8. Simmer on low for an additional 10 minutes, or until the soup has thickened.
9. Taste and adjust seasoning as needed. Optional: Remove the soup from heat and mix in the shredded cheese. Cover and let it melt for 5 minutes before serving!
10. Garnish with fresh parsley, if desired. Note – The soup will thicken as it cools.