In a large pot, heat 1 tablespoon of sesame oil over medium heat. Add the sliced shitake mushrooms and sauté until they begin to caramelize and brown around the edges. Once cooked, transfer the mushrooms to a separate bowl and set them aside.
In the same pot, add the remaining tablespoon of sesame oil. Toss in the minced garlic and sauté briefly—just until it becomes fragrant and golden, about 1 minute.
Pour in 4 cups of chicken broth and bring it to a boil. Stir in the turmeric, brown sugar, fish sauce, soy sauce, chili paste, and red curry paste. Mix well to combine all the aromatic and savory components.
Once the mixture is boiling, pour in the coconut milk. Stir thoroughly and bring the broth back to a gentle boil.
Add the ramen noodles directly into the broth. Cook for about 2 minutes, or just until the noodles are tender but not overcooked.
Ladle the hot, spicy coconut curry ramen into bowls. Top each serving with the sautéed mushrooms, freshly sliced green onions, a sprinkle of sesame seeds, and a soft-boiled egg. Serve immediately while piping hot.