Warm milk in a saucepan over medium heat. Add 2/3 cup sugar and stir to dissolve, about 3 minutes. Make sure milk does not boil; turn off heat if necessary.

Whisk eggs and egg yolk by hand; do not overmix. Pour slowly into the warm milk-sugar mixture and stir continuously over low heat for 90 seconds.

Strain through a tightly woven mesh strainer into a bowl to remove any solids. Add vanilla extract to the bowl; mix until well combined. Set aside.

Pour 1 cup sugar into a wide skillet over medium heat. Stir occasionally until sugar has evenly melted and turned a golden caramel color, about 5 minutes. Immediately remove from heat and pour into a pressure cooker-safe cake pan, coating the bottom with liquid sugar. Pour in custard and cover with aluminum foil.

Place a trivet in the bottom of a multi-functional pressure cooker (such as Instant Pot) and add 1 cup water. Place the cake pan onto the trivet and close the lid. Seal the valve, select high pressure, and set timer for 9 minutes. Allow 10-15 minutes for pressure to build.

Release pressure using the natural-release method for 10 minutes, then turn valve to Venting to release remaining pressure. Remove the trivet and pan from the Instant Pot.