Combine cooked rice, 2 cups milk, sugar, and salt in a multi-functional pressure cooker (such as Instant Pot®) and stir well. Close and lock the lid. Select porridge function according to manufacturer's instructions and seal the vent. Set timer for 20 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Unlock and carefully remove the lid.
Whisk egg yolks together well in a bowl. Add a small amount of cooked porridge and whisk quickly into yolks. Pour mixture into the pot and stir to combine well with rice. Add heavy cream, remaining milk, and vanilla extract. Stir to combine completely.
Serve rice pudding in individual bowls garnished with cinnamon.