Add 1 cup of water to the bottom of the Instant Pot; place trivet inside. (Note: This is the trivet that came with the Instant Pot.)
Add eggs, cheese, cottage cheese, milk and salt to a blender and blend until smooth. Stir in basil.
Equally divide ham among individual cups in a silicone baby food maker mold. Pour egg mixture equally over ham. Cover with foil and gently place on trivet inside Instant Pot.
Cover Instant Pot, select “Steam” and set timer to 8 minutes. After 8 minutes, allow the Instant Pot to natural release for 10 minutes then do quick release by switching valve to “venting.”
Remove the silicone mold from the Instant Pot and allow to cool completely. Flip the egg bites out of the mold onto a plate. Serve immediately or refrigerate in an airtight container for up to 4 days.