Press the Saute button on the Instant Pot. Melt the butter, then add the diced onion and saute until tender, 2 to 3 minutes.
Add the garlic and saute for 30 seconds, until fragrant. Press the cancel button.
Stir in 3 3/4 cups of broth, broccoli, carrots, salt, pepper and nutmeg.
Close and secure the lid and seal the venting knob. Cook on Manual HIGH Pressure for 1 minute.
When the cook time ends, perform a Quick Pressure release; remove the lid carefully. Use an immersion blender to puree some of the soup if you'd like it a bit smoother, then press the Saute button.
In a small bowl, whisk together the corn starch and remaining broth until smooth. When the contents of the pot are simmering, slowly add in the cornstarch mixture. Allow it to simmer, stirring frequently until the soup thickens.
Press Cancel. Stir in the cream and milk. Add the cheese 1/2 cup at a time, stirring until it melts.
Taste and season to your liking, then serve hot.