Adjust an oven rack to the middle position and heat the oven to 375°F (190°C).
Hard-boil 2 of the eggs by covering them with 1 quart water in a small saucepan and bringing to a boil over high heat. As soon as the water reaches a boil, remove the pan from the heat, cover, and let sit for 10 minutes. Meanwhile, prepare a bowl of ice water. Transfer the eggs to the ice water and cool for 5 minutes. Peel the eggs, cut crosswise into 1/4-inch slices, and set aside.
Meanwhile, slice the corn kernels from the cobs. Process half of the corn (about 4 cups kernels) in a blender (or food processor) with the cream until smooth, about 30 seconds. Add the remaining 2 eggs and blend until combined, about 5 seconds. Set aside.
Melt 2 tablespoons of the butter in a 10-inch cast iron skillet over medium heat. Add the onion, celery, and salt and cook, stirring occasionally, until softened, 5 to 7 minutes. Stir in the garlic and pepper and cook until fragrant, about 30 seconds. Off the heat, stir in the remaining corn kernels, corn-cream mixture, and parsley. Smooth the surface of the filling, then arrange the sliced eggs over the top in an even layer. Using your hands, break up the remaining 2 tablespoons butter into small pieces and scatter evenly over the top.
Roll out the dough on a lightly floured counter to a 12-inch circle, about 1/8 inch thick. Cut three oval-shaped vents, each about 1 inch long and 1/2 inch wide, in the center of the dough. Working quickly, roll the dough loosely over the rolling pin and unroll it evenly over the skillet. Trim the dough, leaving 1/2 inch hanging over the pan lip. Press the dough firmly to seal it to the lip of the pan. (For a decorative border, press the edges of the pie with the tines of a fork.)
Place the skillet on a foil-lined rimmed baking sheet and bake until the filling is bubbling and the crust is golden brown, about 1 hour. Cool for 10 minutes before serving the pie.