Fill a medium saucepan half full with hot tap water. Add 1 teaspoon kosher salt and place over medium heat. Gently place the eggs in the water and bring to a boil (starting with hot water makes it easier to peel the eggs). Reduce heat and simmer for 10 minutes. Remove the eggs from heat and plunge into cold water. When the eggs are completely cool, peel and grate them using the large grate of a handheld grater.
Combine the mayonnaise, mustard, curry powder, and paprika in a medium bowl. Add the eggs, watercress, tomatoes, and radish. Season with kosher salt and pepper to taste.
Divide the egg salad evenly among the tortillas and wrap . Enjoy this wrap immediately.