Warm the butter in a saucepan over medium heat until fully melted. The butter should look fluid and lightly foamy, not browned.

Add the onion and celery, then cook for 5 minutes. They should soften and smell sweet and savory rather than sharp.

Stir in the minced garlic and cook for 30 seconds more. You want the garlic fragrant, not dark or toasted.

Add the broccoli, broth, cream cheese, smoked paprika, salt, and black pepper. The cream cheese will begin to soften into the hot liquid as the broccoli starts to brighten.

Cover the pot and let the soup simmer for 8 to 10 minutes. The broccoli should turn vibrant green and become tender enough to pierce easily.

Transfer half of the soup carefully to a blender and puree it. Blend until smooth enough to thicken the broth while leaving the rest chunky.

Pour the pureed portion back into the saucepan and stir in the heavy cream. The soup should look creamier right away and slightly lighter in color.

Add the cheddar and cook for 3 to 5 minutes, stirring until melted. Keep the heat gentle so the cheese melts into the soup instead of turning grainy.

Stir in the white wine vinegar and taste for seasoning. The finished soup should taste rich, sharp, and balanced rather than heavy.

Set the Instant Pot to sauté and melt the butter over medium heat. The butter should be fully melted before the vegetables go in.

Add the onion and celery, then cook for 5 minutes. They should soften and release a mellow, savory aroma.

Stir in the minced garlic and cook for 30 seconds. Stop as soon as it smells fragrant so it does not scorch.

Add the broccoli, broth, cream cheese, smoked paprika, salt, and black pepper to the pot. The cream cheese may look chunky at this stage, which is fine.

Lock the lid and make sure the valve is sealed. The pot should be fully closed before pressure cooking begins.

Set the pot to Pressure Cook on high pressure for 2 minutes. This short cook keeps the broccoli tender without turning it dull.

Let the pressure release naturally for 5 minutes, then do a quick release. Wait until the pressure pin drops before opening the lid.

Open the pot carefully and switch the setting back to sauté. The soup should look hot and the broccoli should be very tender.

Blend half of the soup in a blender, then return it to the pot. This gives you a thicker, velvety base while leaving some broccoli pieces intact.

Stir in the heavy cream and cheddar, cooking and stirring often until the cheese melts. Keep the heat moderate so the soup stays smooth and glossy.

Finish with the white wine vinegar and adjust the salt and pepper if needed. The flavor should pop a little more after the vinegar goes in.