Preheat oven to 400ºF.
In a medium saucepan over medium heat, warm the milk just until bubbles form around the edges.
Sift the flour and salt together in a bowl. Set aside.
In a separate large bowl, whisk the eggs until frothy, and then slowly whisk the warm milk into the eggs, whisking constantly so eggs don't cook. Whisk in the flour mixture just until combined, then whisk in 1 cup of the cheese and the chives.
Place the popover pan in the oven for 2 minutes to heat. Remove it and add a pat of butter to each cup.
Once the butter has melted, portion the batter into the cups, filling each about 3/4 full.
Top with a portion of the remaining cheese.
Bake the popovers for 20 minutes, then reduce the oven temperature to 300ºF, and continue baking about 10 more minutes. (See Notes.)
Remove the popovers from the oven and serve warm.
When measuring flour, never scoop the cup into the flour, as it condenses the flour and causes you to use more than the recipe intends. Instead, spoon the flour into your measuring cup and level it with a knife.
The key to perfectly puffed popovers is to keep the oven closed during the entire baking process. As tempting as it is to peek, keep that door shut!