Start by boiling a large pot of water. Once boiling, add the 6 ounces of ramen noodles. Cook according to package instructions until al dente, usually about 4-5 minutes. Drain and set aside.
In a large skillet, heat 1 tablespoon of olive oil over medium heat. Add the sliced shiitake mushrooms and sauté for about 3-4 minutes until they start to soften. Then, add the minced garlic and shredded carrots, cooking for another 2-3 minutes until fragrant and tender.
In a small bowl, whisk together the ½ cup of low sodium soy sauce, 2 tablespoons of toasted sesame oil, 2 tablespoons of honey, and 1 ½ tablespoons of rice vinegar. Once thoroughly mixed, pour the sauce over the sautéed vegetables.
Add the cooked ramen noodles to the skillet with the vegetables and sauce. Gently toss everything together, ensuring the noodles are evenly coated and heated through. This should take about 2 minutes.
In a separate skillet, heat 2 tablespoons of toasted sesame oil over medium heat. Crack in 2 to 4 eggs, depending on how many fried eggs you want. Cook until the whites are set and the yolks are cooked to your liking (sunny-side up or over-easy works beautifully!).
Divide the ramen noodle mixture into bowls, top each serving with a sesame fried egg, and sprinkle with toasted sesame seeds and sliced green onions. Enjoy your 20 Minute Veggie Ramen Noodles with Sesame Fried Eggs!