Season pork with salt and pepper. Add vegetable oil to multi-cooker and set to Sauté on medium. Add pork and sear for five to seven minutes on each side. Remove pork to a plate.
Add garlic and ginger to the multi-cooker and sauté just until fragrant. Add pork back to multi-cooker, along with chicken stock, shiitake mushrooms, soy sauce, mirin, and garlic chili sauce. Close and lock lid. Close vent. Select Pressure Cook on high for 45 minutes.
Once cooking has finished, quick release the steam by opening valve, being careful to release the steam away from you. Leave multi-cooker on Warming setting.
Using a slotted spoon, remove pork from the broth, then use two forks to shred. Set shredded pork aside on a plate. Add brown sugar to a wok on the stove over medium-high heat and cook, stirring constantly, until it has melted and become a dark syrup, about two minutes. Add pork to wok and turn heat to high, then cook for another minute, stirring constantly. Remove from heat.
Add sesame oil to broth in multi-cooker. Set to Sauté and bring broth to a simmer. Let simmer for five minutes.
In the meantime, bring a pot of salted water to a boil. Add ramen and cook for two to three minutes, until al dente, then drain.
Divide noodles evenly between serving bowls. Pour broth over top. Top each bowl with sliced green onions, sesame seeds, two egg halves, and caramelized pork, making individual piles of each around the bowl.