Heat the vegetable oil in a large cast-iron skillet over medium-high heat until very hot. Add the onions and cook until just starting to soften, about 4 minutes. Add the garlic and cook until fragrant, about 30 seconds. Add the ground turkey and then sprinkle in the salt, paprika and garlic powder. Cook, breaking up clumps of the turkey with a wooden spoon, until brown, about 6 minutes. Add the gravy, corn, lima beans, parsley, Worcestershire sauce and hot sauce. Reduce the heat to a simmer; simmer for about 3 minutes.
While the filling simmers, stir together the potatoes, cheese and eggs in a large bowl, making sure it is thoroughly mixed. Layer the potatoes on top of the filling in the skillet. Bake the shepherd's pie until bubbling and golden brown, 30 to 45 minutes.