Add the eggs, ricotta, sour cream, salt, and pepper to a food processor or blender and process until smooth. Spray a silicone egg bite tray with cooking spray. Divide the ham between the wells of the tray. Pour the egg mixture over the ham, filling the wells of the tray evenly. Sprinkle each of the wells with cheese. Cover the egg bite tray with foil.

Place the trivet in the instant pot and add 1 cup of hot water to the pot. Carefully place the egg bite tray in the instant pot. Close the lit and turn the knob to seal. Cook using the steam function for 9 minutes, then let the pressure release for 10 minutes. Release the remaining pressure, then carefully lift the egg bite tray from the pot using the handles of the trivet. Remove the foil and run a plastic knife around the edges of the egg bites to release them from the tray. Invert the egg bites onto a plate or platter. Serve warm or refrigerate until ready to eat.