Use saute mode to preheat the Instant Pot.
Once hot, add 1 tbsp of butter to melt. Then add the leeks and garlic and saute until the leeks are translucent—about 5 minutes.
Add the broccoli and broth and season with salt and pepper. Secure the lid of the Instant Pot.
Select Manual mode and cook at high pressure for 6 minutes.
While the soup cooks, melt the remaining 3 tbsp butter in a small saucepan on the stovetop. Whisk in the flour until a paste is formed, then add the milk. Cook until thick and bubbly, stirring frequently.
Once pressure cooking is complete, use natural release (wait for the pin sink down on its own).
Add the parmesan. Puree the broccoli and broth using an immersion blender.
Add the milk mixture to the broccoli, stirring well. Taste and adjust seasoning. Serve with a sprinkle of parmesan on top.