In a medium bowl combine soy sauce, hoisin sauce, hot mustard, rice vinegar, chili oil, brown sugar, garlic, ginger, and ½ teaspoon red pepper flakes. Mix well and set aside.
Julienne carrots and celery. Slice the green onions. Place the beef strips into a medium bowl. Add the cornstarch and toss to coat. Make sure each piece is thoroughly coated. Set aside for 10 minutes. Heat ¼ cup of peanut oil in a wok or large skillet over medium-high heat. Add the sliced beef and fry until crispy (about 3-5 minutes) and done to your liking.
Remove with a slotted spoon and drain on a plate lined with paper towels.
Drain the oil from the wok. In the same pan used to cook the beef, add sesame oil over medium-high heat.
Add celery and give it a good stir, then add ½ teaspoon crushed red pepper flakes and stir again, and then add carrots and stir. Stir-fry the vegetables for 30 seconds.
Add the fried meat and green onions. Pour in the sauce mixture and bring to a boil. Cook for 1 minute.