In a medium bowl, mix together the turkey, egg, garlic, scallions, ½ teaspoon of the salt, the pepper and sage. In a large (12-inch) skillet over medium heat, heat the oil until shimmering. Add the turkey mixture and cook, stirring occasionally and breaking the meat up with a wooden spoon, until browned and no pink remains, 6 to 8 minutes. (While the turkey mixture is cooking, wash and dry the bowl you just used.) Transfer the turkey mixture to the now-clean bowl and add the green beans.
Wipe out the skillet and return it to medium heat. Line a large plate with towels and set it near your work space. Add the bacon to the skillet and cook, turning over as needed, until crisp, 8 to 10 minutes. Adjust the heat as needed to prevent the bacon from burning. Transfer the bacon to the prepared plate, let cool completely, then coarsely chop. Using a slotted spoon, add the bacon to the bowl with the turkey and green beans, leaving the bacon grease in the skillet, and gently mix to combine. Transfer the mixture to a 9-by-13-by-2-inch baking dish and spread in an even layer.
Position a rack in the middle of the oven and preheat to 375 degrees.
While the bacon is cooling, return the skillet with the bacon grease to medium-high heat. Add 1 tablespoon of the butter and once it’s melted and the foam begins to subside, add the mushrooms and cook, stirring frequently, until they release their liquid and it evaporates and the mushrooms brown, 4 to 6 minutes. Transfer the mushrooms to a small bowl.
Return the skillet to medium heat. Add the remaining 4 tablespoons of butter and let it melt. Evenly sprinkle the flour into the butter and whisk to incorporate. Cook, stirring constantly, until the flour is cooked out and the roux is light brown, about 2 minutes. Slowly whisk in the milk and half-and-half, and cook, whisking constantly, until steam starts to rise off the surface of the mixture and it thickens to the consistency of heavy cream, 2 to 4 minutes. Add the cooked mushrooms, onion and the remaining ½ teaspoon of salt, and season to taste with pepper. Cook, stirring, until well combined, about 1 minute. Add about 2 ½ cups (10 ounces) of the cheese and cook, stirring constantly, until melted and the mixture is thick and uniform, about 1 minute, then remove from the heat.
Pour the cheese mixture evenly over the turkey mixture in the baking dish. Arrange the Tater Tots over the top, then sprinkle with the remaining ½ cup (2 ounces) of cheese. Bake for about 45 minutes, or until golden brown and bubbling around the edges. Remove from the oven and let sit for about 10 minutes before serving.