Brown the chicken. Select the Sauté setting on the Instant Pot. Once the pot is hot, add the cooking oil. Brown the chicken in a single layer for 2–3 minutes per side, working in batches if necessary. Transfer the browned chicken to a plate.
Sauté the onion and garlic. Add the chopped onion to the pot and cook for 1–2 minutes, or until it begins to soften. Add the crushed garlic and cook for about 30 seconds, just until fragrant.
Deglaze the pot. Pour in the water. Use a wooden spoon or silicone spatula to loosen any browned pieces from the bottom of the pot.
Add the sauce ingredients. Pour in the soy sauce, vinegar, and oyster sauce. Add the sugar, whole black peppercorns, and bay leaves. Stir gently, then return the chicken and any collected juices to the pot.
Pressure-cook the chicken. Secure the lid and move the steam-release valve to the Sealing position. Select Pressure Cook on high pressure for 7 minutes.
Release the pressure. When the cooking cycle ends, allow the pressure to release naturally for 10 minutes. Carefully move the valve to Venting to release the remaining pressure. Once the pin drops, open the lid and transfer the chicken to a plate.
Reduce the adobo sauce. Select Sauté and simmer the sauce uncovered for 5–10 minutes, stirring occasionally, until it reaches your preferred consistency.
Finish with butter. Turn off the Instant Pot and stir in the butter until completely melted. Taste the sauce and adjust the seasoning if needed.
Coat and serve. Return the chicken to the pot and turn each piece in the reduced sauce until evenly coated. Serve hot with steamed white rice.