Set your Instant Pot to Sauté mode. Add butter and let it melt, then toss in the diced onion. Cook for 3-4 minutes until it's soft and translucent.
Add the minced garlic and cook for another minute until fragrant. Sprinkle in the flour and stir constantly for about 1 minute to create a roux.
Slowly pour in the chicken broth while stirring to prevent lumps. Turn off Sauté mode.
Add the broccoli florets, shredded carrots, salt, pepper, and nutmeg. Stir everything together.
Secure the lid and set the valve to Sealing. Cook on High Pressure for 5 minutes.
When cooking time is complete, do a quick release by carefully turning the valve to Venting.
Open the lid and stir in the half-and-half. For a smoother soup, use an immersion blender to partially blend (leave some chunks for texture!).
Add the shredded cheddar cheese one cup at a time, stirring until melted and smooth. Taste and adjust seasonings as needed. Serve hot with crusty bread or croutons!