Save the flavor packet from your ramen for another use. Slideshow: More Chicken Soup Recipes
In a large heavy pot, heat the oil over medium high heat until hot. Season the chicken with 1 teaspoon salt and 1/2 teaspoon pepper, then brown in batches until golden, about 6 minutes per batch. Transfer the chicken to a platter as browned.
Stir the garlic and ginger into the pot and cook, stirring until golden, about 3 minutes. Stir in the stock and chicken with any accumulated juices and bring to a simmer. Stir in the broccoli and cook until the chicken is cooked through and the broccoli is tender, about 10 minutes. Stir in the ramen and cook until tender, about 3 minutes. Season the soup with salt and pepper to taste and serve sprinkled with the sesame seeds.