Heat the oven to 375°F. Lightly grease a baking dish with a little of the measured ketchup, then set it aside.
Cut the bell peppers in half lengthwise and remove the stems, seeds, and membranes. Arrange the halves cut side up in the baking dish.
In a large bowl, combine the ground turkey, cooked brown rice, egg, breadcrumbs, onion, Worcestershire sauce, oregano, salt, black pepper, and 1/4 cup of the ketchup. Mix gently until evenly combined.
Divide the turkey mixture among the pepper halves, mounding it slightly. Stir the remaining 1/4 cup ketchup with the water, then spoon it over the filling.
Cover the dish tightly with foil and bake for 35 minutes. Remove the foil and bake for another 15 to 20 minutes, until the peppers are tender and the turkey filling reaches 165°F in the center.
Let the stuffed peppers rest for 5 minutes before serving so the filling can settle.