Turn Instant Pot to the "Saute" setting. Add butter and once melted, add garlic and white onions. Cook, stirring occasionally, until fragrant. Avoid browning and burning garlic and onions. Add chicken broth. Stir and scrape the bottom of the Instant Pot to remove anything stuck to it. Add carrots, celery, red Idaho potatoes, chicken breast, dried thyme, dried sage, dried marjoram, and 1 1/2 teaspoon salt. Stir and cover with the lid.
Set Instant Pot to the "Pressure Cook" setting. Cook on high for 15 minutes. Move the valve to the sealing position. When done cooking, release the pressure manually.
Open the lid, and transfer chicken breast to a plate. Discard skin and bones, and shred chicken.
In a small bowl, whisk together milk and all-purpose flour. Set Instant Pot® to the "Saute" setting. Bring to a boil. Add egg noodles and cook accordingly to package instructions. Add the milk and flour mixture. Once egg noodles are cooked and soup is thickened, add the shredded chicken back to the pot. Stir. Taste the soup and add more salt to open up flavors if needed.
Turn off the Instant Pot. Serve soup and garnish with black pepper and parsley.