Trim excess skin and fat from the chicken thighs, then pat them dry.
Season the skin side of the thighs evenly with 1 teaspoon salt, 1/2 teaspoon black pepper, 1 teaspoon paprika, and 1 teaspoon dried oregano.
Place the stainless steel insert in the Instant Pot and select the Sauté function. Heat for 2–3 minutes until hot.
Add 1 tablespoon olive oil and 1 tablespoon butter to the insert. When the butter is melted and sizzling, stir in 1 teaspoon minced garlic.
Arrange the chicken thighs skin-side down in the hot insert and brown for 2–3 minutes until golden and flavorful, taking care not to burn them.
Flip the thighs and cook the other side for 1 minute, then press Cancel and transfer the chicken to a plate.
Pour 1 cup water into the insert and use a wooden spoon to scrape up any browned bits from the bottom.
Place the trivet in the Instant Pot and arrange the chicken thighs on top of the trivet.
Close the lid, set the valve to sealing, select Manual (or Pressure Cook) and set the timer for 12 minutes. The pot will come to pressure and cook.
When cooking completes, press Cancel and allow a natural pressure release for at least 5 minutes (longer if desired), then carefully open the lid and transfer the chicken to a plate to rest.
Remove the trivet. In a small bowl, whisk 1 tablespoon cornstarch with 1/4 cup water until smooth, then add the slurry to the liquid in the insert and stir to combine.
Use the Sauté function and simmer, stirring, until the sauce thickens to a gravy consistency; then serve the chicken with the gravy.
