Set the Instant Pot to the sauté mode. Add the unsalted butter and allow it to melt. Once melted, add the diced onion and sauté for 2-3 minutes until tender.
Stir in the minced garlic and sauté for an additional 30 seconds until fragrant.
Pour in the vegetable or chicken broth, then add the broccoli florets, diced carrots, salt, pepper, and nutmeg. Stir to combine all ingredients.
Close the lid, confirm the valve is set to sealing, and choose Manual HIGH Pressure. Set the timer for 1 minute.
Once the cooking time is complete, perform a Quick Pressure Release by carefully turning the valve to venting. Once the pressure has released, open the lid and use an immersion blender to partially blend the soup to your desired consistency.
In a small bowl, mix the cornstarch with a couple of tablespoons of the warm broth from the pot until smooth. Stir this mixture back into the soup.
Then, add the heavy cream, milk, and freshly grated cheddar cheese, stirring until the cheese is melted and the soup is creamy.