Set the Instant Pot to Saute mode and add the butter. Once melted, add the diced onion and saute for 3-4 minutes until softened. Add the minced garlic and cook for 30 seconds.
Pour in the chicken broth and stir, scraping up any bits from the bottom. Add the broccoli florets, diced carrot, salt, black pepper, and nutmeg.
Lock the lid, set the valve to Sealing, and cook on High Pressure for 3 minutes.
Perform a quick release by carefully turning the valve to Venting, keeping hands and face clear of the steam. Remove the lid once the pin drops.
Use an immersion blender to partially blend the soup, leaving some chunks of broccoli for texture. Alternatively, transfer about 2 cups to a blender, blend until smooth, and return it to the pot.
Switch to Saute mode. Stir in the heavy cream and the cornstarch slurry. Let the soup simmer for 3-4 minutes, stirring frequently, until it thickens.
Turn off the Instant Pot. Add the shredded cheddar cheese one handful at a time, stirring until each addition is fully melted. Serve immediately in bread bowls or with crusty bread.