In a wide mouthed 1-pint Mason jar, combine the eggs and Laughing Cow cheese. Using an immersion blender, blend for about 15 seconds, just until smooth.
Pour 1 cup water into the Instant Pot. Generously grease 7 silicone muffin cups with butter, making sure to coat all of the ridges well. Place the muffin cups on a long-handled silicone steam rack.
Sprinkle the broccoli and green onions among the muffin cups, then pour in the egg mixture, dividing it evenly and filling each cup about half full. Sprinkle the cups evenly with the Cheddar cheese. Holding the handles of the steam rack, carefully lower the muffin cups into the pot. If necessary, clasp together the handles of the steam rack.
Secure the lid and set the Pressure Release to Sealing. Select the Steam setting and set the cooking time for 8 minutes at low pressure. (The pot will take about 5 minutes to come up to pressure before the cooking program begins.)
When the cooking program ends, let the pressure release naturally for 5 minutes, then move the Pressure Release to Venting to release any remaining steam. Open the pot. The egg muffins will have puffed up quite a bit during cooking, but they will deflate and settle as they cool. Wearing heat-resistant mitts, grasp the handles of the steam rack and lift the muffin cups out of the pot. Let the muffins cool for about 5 minutes, until you are able to comfortably handle them.
To unmold, pull the sides of the muffin cups away from the muffins and transfer the muffins to plates. Serve warm.