In a small bowl, whisk together the stock, fish sauce, sugar and cornstarch.
In a large skillet, heat 2 tablespoons of the oil. Add the shrimp and cook over high heat, turning once, until just white throughout, about 1 minute per side. Transfer to a plate.
Add the remaining 3 tablespoons of oil to the skillet. Add the shallots and ginger and stir-fry over high heat until fragrant, about 1 minute. Stir the stock mixture, add it to the skillet and bring to a boil. Stir in the watercress, then stir in the shrimp and lime juice and season with pepper. Transfer the stir-fry to bowls, sprinkle with the peanuts and serve with rice.