Fill a large saucepan with water and bring to a boil.Add the ramen noodles and cook 3 minutes, breaking them apart with a wooden spoon as they cook.Drain and rinse with cold water and set aside.
In a medium bowl, whisk together the ground ginger, jarred minced garlic, low sodium soy sauce, warm water, packed light brown sugar, corn starch, sesame oil, and black pepper until combined.
Heat a large skillet over medium heat.Add 1 tablespoon olive oil, broccoli and 2 tablespoons water. Cover with a lid and cook 4 minutes, stirring occasionally until crisp tender.Transfer the broccoli to a separate dish.