Put a 12-cup muffin pan (preferably light-colored metal) in the oven and preheat to 400 degrees F.
Whisk the milk, eggs, 1 teaspoon salt and 1/2 teaspoon pepper in a large bowl. Whisk in the melted butter, then whisk in the flour until smooth. Stir in the parsley, chives and rosemary. Let the batter sit at room temperature at least 10 minutes.
Remove the hot muffin pan from the oven and generously brush each cup with vegetable oil. Divide the batter among the cups, filling each about halfway (about 1/3 cup batter per cup). Bake until the puddings rise and are deep golden brown, about 35 minutes. Do not open the oven during baking.
Let them cool 5 minutes in the pan, then remove with a small offset spatula. Serve warm or at room temperature.