Combine the butter, 3 cups milk, sugar, and salt in a heavy saucepan, and heat over medium-high heat. When it comes to a simmer and the butter is melted, reduce the heat to medium-low. Add the cornmeal in a slow, steady drizzle, whisking all the while. Whisk in the corn kernels and cayenne and continue whisking for another 4 or 5 minutes, until the mixture is thick. Remove from the heat and turn into a large mixing bowl.
In a small bowl, whisk together the eggs yolks, and remaining ¼ cup milk, and set aside. In a medium-sized bowl using an electric mixer (or a clean whisk if you have the stamina), beat the egg whites with the cream of tartar until the peaks are stiff, but not dry or separating.
Add about ½ cup of the cornmeal mixture to the bowl with the egg yolks and stir quickly to combine. Turn the yolk mixture into the bowl with the rest of the cornmeal mixture and whisk to combine. Fold about ⅓ of the egg white mixture into the cornmeal mixture, which will lighten the batter, then gently fold in the rest of the egg whites so that they are almost incorporated — you will see a white streak or two, which is fine.
Scrape the batter into the prepared baking dish and bake for about 30 to 35 minutes until the top is browned and puffy. When you shake the pan the spoonbread should juggle slightly, not too much so that it looks liquidy in the middle. Remove and either serve hot to try and capture the spoonbread at its puffiest self or cool slightly on a wire rack, then serve warm.
Notes
Whipping the egg whites until they are fluffy but not dry or separating. It is an extra step, but one that ensures that the resulting dish will be light and fluffy while not missing a beat in the substance department.
In cooking, folding is the gentle blending of a lighter ingredient with a heavier one, in this case the fluffy beaten egg whites with the heavier cornmeal corn mixture. The lighter component is added in batches, and a spatula is used to pull up the heaver mixture up and over the lighter ingredient until they are just barely combined. It is not stirring, which would deflate the lighter element, but folding the two components together until blended. It's fine to see slight streaks of the egg whites in the blended mixture, which means the mixture has not been overmixed.
When you fold in the egg whites stop before they are fully incorporated – you want to see a white streak or two, which is fine. Overmixing the batter with egg whites will cause them to deflate, and the casserole won't rise as much.
When you shake the pan, the spoonbread should juggle slightly, but not too much so that it looks liquidy in the middle.
You do want to serve this dish warm from the oven so that it holds its slightly soufflé-like texture. It will collapse no matter what (that's what spoonbreads do!), but the faster you serve it, the fluffier it will be.