Preheat oven to 425 degrees with rack in the lower third of the oven. Place a 12-well popover pan (preferred) or a standard, nonstick 12-cup muffin tin into the oven, on a lined baking sheet, to heat.
In a small bowl, stir together goat cheese and chives. Set aside. Measure out flour, salt, and pepper, and set aside.
In a large bowl, vigorously whisk together milk and eggs until frothy, 1-2 minutes. Add flour, salt, and pepper, and whisk until just combined and only small lumps remain. Whisk in melted butter. Batter will be relatively thin, with the texture of cream.
Remove popover pan from oven and coat wells with cooking spray. Fill each well about halfway with batter. Spoon about 1 teaspoon of goat cheese into the center of each well and sprinkle with some of the crumbled bacon.
Bake for 20 minutes, then reduce oven temperature to 350 degrees F and continue baking for about 15 minutes, until popovers are golden and tops are dry. Popovers will rise considerably.
Immediately remove popovers from pan and use a sharp knife to pierce the sides of each to allow the steam to escape. For the crispiest exteriors, serve immediately.
Using room temperature ingredients is very important to achieve popovers with the best texture and rise. If time is of the essence, the milk can be microwaved until just warm and the eggs can be placed in a bowl of warm water for 10 minutes.