In a medium bowl, whisk together the gluten free flour blend, tapioca starch, salt, and black pepper. Make a well in the center.
Crack the eggs into the well and pour in the milk. Whisk from the center outward, gradually incorporating the flour until you have a smooth, thin batter with no lumps. Let the batter rest at room temperature for at least 30 minutes.
Preheat the oven to 425 degrees F. Add about 1 teaspoon of vegetable oil into each cup of a 12-cup muffin tin. Place the tin in the oven for 10 minutes until the oil is smoking hot.
Carefully remove the tin from the oven. Working quickly, pour the batter evenly into the cups, filling each about halfway. The oil should sizzle when the batter hits it.
Immediately return the tin to the oven. Bake for 20 to 22 minutes until the puddings are puffed, tall, and deep golden brown. Do not open the oven door during baking.
Remove from the oven and serve immediately while still puffed and crispy. These are perfect alongside roast beef and gravy.