Bring a medium saucepan to medium heat. Add a small drizzle of oil and sauté the shallot until soft and fragrant, about 3 minutes. Add the garlic and stir for 30 seconds. Immediately stir in the grated ginger, dried chili flakes, and fresh red chili.
Add the coconut cream and broth. Stir well to combine and let the soup simmer for 4 to 5 minutes, until slightly thickened and uniform. Add the sliced mushrooms and simmer for another 5 to 6 minutes until tender.
Meanwhile, boil the noodles in a separate pot of water for 1 minute (or according to package instructions). Prepare the soft-boiled egg in a small saucepan: bring water to a boil, gently lower the egg, and cook for 6 minutes, then transfer to ice water.
To serve, place the noodles in a wide soup bowl. Pour the hot coconut broth and mushrooms over the top. Halve the soft-boiled egg and place it on the noodles. Sprinkle with sliced green onion, cilantro, chili oil, and sesame seeds. Serve hot.