Set Instant Pot to saute.
Add butter and melt.
Once butter is fully melted, whisk in the flour. Continue to whisk until the flour has browned and the butter and flour are fully combine.
Slowly add in the chicken broth, whisking constantly.
Mix in the broccoli, carrots, onion, salt, pepper, and nutmeg.
Close lid and set to sealing.
Program instant pot to soup for 10 minutes.
Natural pressure release for 15 minutes.
Removed lid and pour in the half and half and milk.
Blend with an immersion blender until smooth.
Fold in the shredded sharp cheddar and mix until melted.
Serve in a bread bowl with additional cheese sprinkled on top, if desired.