For the Chicken and Broccoli:In a small bowl, whisk together the sesame oil, hot sauce, garlic, soy sauce, water, sugar, and cornstarch; set aside.Prepare an ice bath for the broccoli by placing a lot of ice in a large bowl of water; set aside.Bring a large pot of salted water to a boil; add the broccoli. Blanch the broccoli for 4 minutes, then immediately transfer the broccoli to an ice bath to stop the cooking process; set aside.Heat the olive oil in a large skillet over medium-high heat. Add the chicken and brown it on both sides. Add the broccoli, reduce the heat to medium, and add the sauce. Stir to coat ingredients and cook for about 5 minutes, or until the sauce has thickened.Meanwhile, make the Lo mein -Begin a large pot of salted water to boil. Once the water reaches a full boil, add the noodles and cook according to the package directions (about 4 minutes).While waiting for the water to boil, prepare the spicy sriracha sauce. In a small bowl stir together the brown sugar, soy sauce, sriracha, ginger, and sesame oil.In a large skillet melt 1 tablespoon of butter over medium-low heat. Add the crushed red pepper to the butter, and once it's completely melted whisk in the eggs. Stir gently and cook for about 3 minutes. Once the egg is done cooking, keep the pan on the burner but transfer eggs to a small plate; set aside.Add 1 tablespoon of oil to the pan and increase the heat to medium-high. Add carrots and snow peas to the pan and stir fry until just charred; about 3 minutes. Stir in the garlic and cook for one minute more.Add drained noodles to the skillet along with the cooked egg and prepared sauce. Turn the heat on to medium-low, and stir until everything is coated well with the sauce. Top the noodles with the chicken and broccoli, sprinkle with the sliced green onions and serve at once!