Add butter to the Instant Pot. Using the display panel select the SAUTÉ function.
When butter is melted, add onion and garlic. Cook and stir until onion is softened, 3-4 minutes.
Add rice and cook, stirring, 1 minute more.
Add wine and quickly deglaze by using a wooden spoon to scrape the brown bits from the bottom of the pot, then add 3 cups chicken broth, salt and pepper. Stir to combine.
Secure the lid, making sure the vent is closed.
Using the display panel select the MANUAL function*. Use the +/- keys and program the Instant Pot for 12 minutes.
When the time is up, quick-release the remaining pressure. Select CANCEL to turn the pot off, then select the SAUTÉ function.
Stir in the shrimp and the remaining 1 cup of broth. Cook, stirring occasionally, until the shrimp are opaque, 3-5 minutes. Stir in cheese until melted, then fold in herbs. Serve immediately.
Notes
*The Manual and Pressure Cook buttons are interchangeable.