Heat the sesame oil in a large saucepan over medium heat. When the oil is hot, add the garlic and ginger and let them simmer for about 30 seconds, stirring often.
Add the shiitake mushrooms and sauté until they've softened, about 2-3 minutes.
Spoon the chili paste into the pot, then stir it around to coat the mushrooms.
Add the soy sauce, rice wine vinegar, salt, and sugar. Give it a quick stir, then pour the chicken and dashi stock into the pot; stir again.
Allow the soup to simmer for about 15 minutes. While it simmers, cook your ramen noodles, your egg (see notes), and prepare your toppings.
After the soup has simmered for about 15 minutes, give it a taste test and adjust the heat and soy sauce to your liking.
Strain the noodles when they're ready, then transfer them to a large bowl. Spoon broth over the noodles in the bowl, and then garnish with your toppings.