Season the chicken thighs evenly with kosher salt and black pepper on both sides.
Set the Instant Pot to ‘Sauté’ mode and heat the olive oil.
Add the chicken thighs skin-side down and cook for 4-5 minutes until the skin is golden brown. Flip and cook the other side for 3 minutes. Remove the chicken and set aside.
Add the sliced onion to the Instant Pot and sauté for 2 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the carrots and red potatoes to the pot and stir to combine with the onions and garlic.
Pour in the chicken broth, scraping the bottom of the pot with a wooden spoon to deglaze and remove any browned bits.
Sprinkle the dried thyme, dried rosemary, smoked paprika, and crushed red pepper flakes over the vegetables and broth. Stir to combine.
Place the browned chicken thighs on top of the vegetables in a single layer.
Secure the Instant Pot lid and set the valve to the ‘Sealing’ position.
Select ‘Pressure Cook’ or ‘Manual’ mode and set the timer for 12 minutes.
When the cooking time is complete, allow the pressure to release naturally for 10 minutes, then carefully turn the valve to ‘Venting’ to release any remaining pressure.
Open the lid and check that the chicken thighs have reached an internal temperature of 165°F (74°C).
Transfer the chicken and vegetables to serving plates and spoon some cooking liquid over the top.
Garnish with chopped fresh parsley and serve immediately.