Fill a medium saucepan with 1 inch of water. Place a steamer basket in the saucepan and place the spinach in the basket. Cover the pot, bring the water to a simmer, and steam the spinach until wilted, about 3 minutes. Drain the spinach in a colander, pressing out any excess moisture.
Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F). Preheat the griddle over direct medium heat for 5 minutes.
Prepare the grill for direct and indirect cooking over medium heat (400°F). Preheat the griddle over direct medium heat for 5 minutes.
Melt the butter in the griddle over direct medium heat. Add the leeks and cook until soft, about 5 minutes, stirring occasionally with a wooden spoon.
Spread the turkey and spinach evenly over the leeks. Pour the eggs over and lightly stir to blend.
Wearing protective gloves, place a large foil pan on top of the Flavorizer bars on the left side of the grill, below the cooking grate. Fill it halfway with room-temperature water. Prepare the grill for cooking over medium heat (400°F).
Slide the griddle over indirect medium heat. Close the grill lid and cook until the eggs are puffed, set, and golden in spots, 15 to 18 minutes. Serve warm or at room temperature.
Slide the griddle over indirect medium heat. Close the grill lid and cook until the eggs are puffed, set, and golden in spots, 15 to 18 minutes. Serve warm or at room temperature.