Preheat oven to 425°F. Set rack in the center of the oven.
In a heavy skillet, melt 1 1/2 tablespoons of olive oil and sauté the onion with a pinch of salt over medium-low heat until translucent. Increase the heat, add the mushrooms and sauté for about two minutes. Add soy sauce and continue to sauté until the mushroom liquid is evaporated. Remove from heat.
Stir in the 3/4 cup gravy, eggs, ham and kale. Season to taste with salt and pepper.
Spread a layer of tater tots in a baking dish. Transfer the filling mixture into the baking dish and top with shredded cheese.
Arrange more tater tots on top, lightly cover with foil, and place in the oven. Bake for about 30 minutes. Remove foil, lower oven temperature to 350°F and bake for another 15 minutes until the filling is bubbling and the tater tots are golden brown.
Serve immediately with remaining gravy, and enjoy!