Mince the garlic cloves and set aside. Pat the chicken thighs dry with paper towels, then season both sides generously with salt and pepper. Slice the roasted red peppers into 1/2-inch strips, quarter the artichoke hearts, halve the kalamata olives, and thinly slice the red onion into half-moons. Having everything prepped and ready will allow the cooking process to move smoothly once you start.
Set your Instant Pot to sauté mode and heat the olive oil until shimmering. Add the minced garlic and let it toast for about 1 minute, stirring occasionally, until fragrant—this blooms the garlic and releases its essential oils for deeper flavor. Working in batches if needed to avoid overcrowding, sear the seasoned chicken thighs for 2 minutes on each side until they develop a light golden crust. This browning creates fond (the flavorful browned bits) that will enhance the final sauce.
In a small bowl, whisk together the chicken broth, red wine vinegar, lemon juice, dried oregano, dried thyme, and honey (if using). I find that the honey balances the acidity of the vinegar beautifully, creating a more harmonious sauce. Return the seared chicken to the pot, then arrange the sliced red peppers, quartered artichoke hearts, halved olives, and sliced red onion around and over the chicken. Pour the prepared braising liquid evenly over everything.
Lock the Instant Pot lid in place and set it to high pressure for 7 minutes. Once the timer completes, allow the pressure to release naturally for 5 minutes, then carefully switch the valve to quick-release to vent any remaining steam. Open the lid and check that the chicken is tender and easily pulls apart with a fork.
In a small bowl, whisk the arrowroot starch with 3 tablespoons of the hot cooking liquid until smooth and lump-free. Switch the Instant Pot to sauté mode and slowly pour the slurry back into the pot, stirring gently and continuously for about 2 minutes until the sauce thickens and becomes glossy. I like to cook the starch slurry in the pot rather than letting it sit because this helps it incorporate evenly without lumps. Taste and adjust seasoning with additional salt and pepper if needed.
Transfer the chicken and vegetables to a serving platter or individual bowls. Drizzle the thickened sauce over the top and garnish generously with fresh basil chiffonade, chopped fresh parsley, and crumbled feta cheese. Serve immediately alongside rice, potatoes, or crusty bread to soak up the delicious sauce.