Heat one teaspoon of olive oil and 2 teaspoons of sesame oil in a large pot over medium heat. Cook chicken just until browned. Transfer to a plate.
In the same pot add remaining olive oil, garlic, shiitake mushrooms and ginger. Cook 5 minutes or until mushrooms are soft. Pour in chicken broth, soy sauce and sriracha. Return chicken to pan. Reduce heat to low and let simmer for 25 minutes.
Prepare udon noodles according to package directions.
Divide noodles between bowls and ladle soup over the top. Sprinkle with green onions.
Notes
The stems of shiitake mushrooms can be pretty woody so I do recommend removing them. Nutrition information for estimation purposes only.