Use the sauté function of the Instant Pot, or heat a large heavy bottom pot to medium-high heat, and add in the oil. When the pot is ready, add in the chicken drumsticks, trying to get as much skin in contact with the bottom of the pot. Let it cook until the bottom of the skin is browned, then rotate the drumsticks. The chicken should release pretty easily from the pan when it is ready to be rotated. Cook for about 5-7 minutes, rotating as needed, and until the chicken drumsticks are browned all the way around. If the chicken is burning, turn down the heat a bit.
Add in the onions and sauté for about a minute, until the onions start to lightly brown. At this point, the bottom of the pan should also have browned bits, but not burnt.
Add in a bit of water and deglaze the pot completely. Once you've scraped off all the browned bits, add in the remainder of the water, the vegetable or chicken stock, the carrots, the celery, the ginger, and the garlic salt.
If you are using an Instant Pot, set it on low pressure and cook for 15 minutes, with natural release. If you are cooking on the stovetop, bring everything to a gentle boil, then turn the heat down. Cover and simmer for about 30 minutes, stirring occasionally.
In the meantime, cook the egg noodle according to the package instructions. When the noodles are done, drain, rinse in cold water, and set aside. Toss the noodles in a bit of olive oil to prevent it from sticking.
When the chicken soup is done, carefully remove the ginger and chicken drumsticks to a large bowl. Add in the peas and cook the soup for a couple more minutes.
Remove the bones and skin from the cooked drumsticks, and discard them along with the ginger pieces. Gently shred or chop the meat into smaller pieces. Add the meat back into the soup.
Serve the noodles and chicken soup together. Salt and pepper to taste, but I leave out additional salt for younger kids.