Preheat the oven to 375°F (190°C). Position a rack in the center. Grease a 9-inch deep-dish pie plate thoroughly with the softened butter, including the sides. Place the pie plate on a rimmed baking sheet if you want easier transfer in and out of the oven.

If using frozen corn, thaw it completely and drain away any liquid. If using canned corn, drain it thoroughly. For very wet corn, pat the kernels gently with paper towels. The corn should be moist but not dripping.

In a large mixing bowl, whisk the eggs until the yolks and whites are completely combined. Add the whole milk and heavy cream. Whisk until the mixture looks smooth and uniform.

In a small bowl, whisk together the flour, kosher salt, black pepper, smoked paprika, and garlic powder. Gradually whisk this dry mixture into the egg mixture. Continue whisking until no visible flour lumps remain. The custard should be fluid and slightly thicker than plain milk.

Reserve ½ cup (57 g) of the shredded cheddar and about 2 tablespoons of the sliced scallions for the top. Add the remaining cheddar, remaining scallions, and all of the corn to the custard. Fold gently with a rubber spatula until the ingredients are evenly distributed.

Pour the mixture into the prepared 9-inch pie plate. Use the spatula to distribute the corn evenly so it does not collect in one area. Sprinkle the reserved cheddar over the surface, followed by the reserved scallions.

Bake at 375°F (190°C) for 35–40 minutes. The edges should be golden and slightly puffed, while the center should look set with only a gentle wobble when the pie plate is moved. If the cheese on top begins browning too quickly, loosely cover the surface with aluminum foil during the final 10 minutes.

Insert a thin knife into the center: It should come out mostly clean without liquid egg custard. For a more precise check, the center should reach at least 160°F (71°C) because the filling contains eggs. Avoid overbaking, which can make the custard rubbery and cause moisture to separate around the edges.

Remove the pie from the oven and place it on a wire cooling rack. Let it rest for 15 minutes before slicing. The filling will continue to set as it cools, making the wedges easier to lift cleanly.

Sprinkle with the optional chopped parsley: Cut the pie into 8 wedges and serve warm or at room temperature.