Heat the Instant Pot using the Saute-Low function.
Add the sesame oil, olive oil, honey, garlic clove, and red pepper flakes.
Cook for 3-5 minutes, stirring occasionally, or until the garlic clove is starting to turn golden brown.
Transfer the oil to a jar and set aside. There is no need to rinse out the pan from the chili oil, it will add more flavor!
Add the olive oil and heat the Instant Pot using the Saute-Normal function. When the oil is hot, add the chicken thighs, skin side down. Cook for 3-5 minutes, or until the chicken skin is golden brown and can be removed from the pan without sticking.
Flip the chicken thighs and cook for an additional minute.
Remove the chicken thighs from the Instant Pot and add the sliced mushrooms. Cook the mushrooms, stirring occasionally, for 1-2 minutes, or until they start to turn golden brown. Add the ginger and garlic and cook for an additional minute.
Add the chicken stock, soy sauce, green onion, rice vinegar, and chicken thighs to the Instant Pot. Using a wooden spoon, scrape the browned bits from the bottom of the pot.
Turn the Instant Pot to Manual Pressure and cook on high pressure for 10 minutes. Make sure the valve on the lid is turned to the “sealing” position.
The Instant Pot will take a few minutes to come to pressure and then begin counting down from 10. When the Instant Pot has finished cooking, carefully release the pressure manually by switching the valve to the “venting” position. Be careful when opening the valve, it will steam and may splatter.
Remove the chicken and set aside, allowing to rest for at least 5 minutes.
Turn the Instant Pot to the Saute function. Add the cleaned eggs (if using) and cook for 8 minutes.
Check the cook time on your ramen noodles. Add the noodles into the pot with the broth while the eggs are cooking. My ramen cooks in 4 minutes so I allowed the eggs to cook for 4 minutes, then added the ramen and continued cooking them together for 4 minutes.
Remove the eggs to an ice bath to stop the cooking process. Gently peel them and set aside.
Slice the chicken and add it back to the ramen. Serve hot with a drizzle of sweet chili oil, sliced green onions and lime wedges.