Over medium-low heat, warm the sesame oil in a medium saucepan until it's hot. Add the shredded carrots, sliced mushrooms, and any other chopped veggies you'd like. Simmer until the veggies are tender, about 2-3 minutes.
Add the garlic and ginger to the saucepan; simmer for 30-45 seconds until fragrant.
Pour the broth into the pot. Add the soy sauce, rice vinegar, and Sriracha if you're using it. Stir the broth well and let it simmer on low for five minutes. Give it a taste and adjust the soy sauce or hot sauce as needed.
While the soup is simmering, you can cook the Ramen noodles in a separate pot according to the package's instructions. When the noodles are cooked, drain and rinse them under cool water, then transfer them to soup bowls.
With a ladle, spoon the broth over the noodles in the bowls. Garnish with your preferred toppings and serve.
*See the notes below for instructions on cooking a soft-boiled egg.