01 - Activate 'Sauté' mode on the Instant Pot. Melt unsalted butter, then add diced onion, minced garlic, grated carrot, and diced celery. Sauté for 3 to 4 minutes, stirring occasionally until vegetables are softened and aromatic.
02 - Sprinkle all-purpose flour over sautéed vegetables, stirring thoroughly to coat. Cook for 1 minute to eliminate any raw flour taste.
03 - Add chopped broccoli florets, vegetable broth, salt, ground black pepper, smoked paprika, and freshly grated nutmeg. Mix well to combine ingredients evenly.
04 - Secure Instant Pot lid, set valve to 'Sealing,' and select 'Manual' or 'Pressure Cook' for 4 minutes at high pressure.
05 - Quick-release pressure when cooking completes. Carefully remove the lid and stir the contents.
06 - Use an immersion blender directly in the pot to purée the mixture to preferred consistency, either leaving some texture or blending until smooth.
07 - Return pot to 'Sauté' mode. Pour in whole milk and heavy cream, heating gently while stirring. Avoid boiling.
08 - Gradually add shredded sharp cheddar cheese, stirring continuously until fully melted and soup is smooth.
09 - Taste and adjust seasoning if desired. Ladle hot soup into bowls and serve immediately.