Preheat the oven to 400 degrees F (200 degrees C).
Heat milk in a small saucepan over medium heat until simmering. Place 2 tea bags in a bowl and pour hot milk on top. Steep for 5 minutes.
Carefully squeeze tea bags to release as much liquid as possible; discard tea bags. Let milk cool completely.
While tea is steeping in the milk, remove tea leaves from remaining tea bag. Grind into a powder using a spice grinder or mortar and pestle. Combine 1/2 the ground tea with confectioners' sugar in a small bowl. Reserve remaining ground tea.
Whisk eggs, flour, tea-infused milk, vanilla extract, and salt together in a large bowl until smooth. Pour batter through a mesh sieve to remove any remaining lumps.
Melt butter in a 10-inch cast iron skillet over medium-high heat. Immediately add apple slices, brown sugar, reserved ground tea, nutmeg, and cinnamon. Cook and stir until apples are tender, 4 to 5 minutes. Pour batter on top and transfer the pan to the preheated oven.
Bake until pancake is set, puffed, and golden brown, 13 to 15 minutes.
Shake skillet to loosen pancake and transfer to a serving plate. Dust with Earl Grey-sugar mixture.
