Melt the butter in a small saucepan over medium heat, then add in the milk, sugar and salt. Stir until the sugar and salt dissolve and the milk is warm to the touch. Remove from the heat. In a medium bowl, whisk together the eggs until they're light and frothy, about 3 minutes.
Sift in the flour, one cup at a time, and whisk until no lumps remain. Cover the batter and let rest for one hour.***
Preheat the oven to 450 degrees, then grease the outer 10 muffin cups on a pan, leaving the inner two cups ungreased. Place the muffin tin in the oven to heat up for about 5-10 minutes.
Remove the muffin tin from the oven, then whisk the batter to recombine. Pour the batter into the cups about ¼ inch away from the top, leaving the middle two cups empty. This will ensure even cooking, and you may have some batter leftover.
Bake, without opening the oven door until browned, about 15-20 minutes. Lower the oven temperature to 300 degrees, and continue to bake for an additional 10 minutes. Use a skewer to poke a small hole in the top of each popover, return to the oven and bake for an additional 5-10 minutes, or until deep golden brown.
Remove popovers from the pan and serve immediately.