Sauté Aromatics: Set the Instant Pot to Sauté mode on High. Heat the sesame oil.
Cook the Vegetables: Once the oil is hot (after about 3 minutes), add the mushrooms, red bell pepper, and garlic. Sauté for another 3 minutes until softened.
Add Broth and Pasta: Pour in the broth, scraping up any browned bits. Break spaghetti in half and place in the pot, submerging it in the liquid but do not stir. Some noodles may stick above the liquid—this is fine. Add butter and tarragon on top.
Pressure Cook: Close the lid, set the valve to Sealing, and pressure cook on High for 8 minutes. Perform a Quick Release once cooking is done.
Prepare the Sauce: While the pasta is cooking, whisk together oyster sauce, hoisin sauce, soy sauce, ginger, and chili-garlic sauce (if using) in a bowl.
Combine & Serve: Open the lid, pour in the sauce, and mix well. Let the noodles sit for 5 minutes to allow the sauce to thicken. Toss in sliced scallions and sesame seeds. Serve warm or enjoy cold!