In a small bowl, whisk together all the sauce ingredients and set aside.
Boil the noodles in a large pot according to package and drain.
Heat olive oil in a large skillet or wok over medium high heat. Add garlic, mushrooms, bell pepper, and carrot. Cook, stirring frequently, until tender, about 3-4 minutes.
Stir in snow peas and spinach until the spinach has wilted, about 2-3 minutes.
Stir in noodles and soy sauce mixture and toss to combine.
Serve immediately.