In a medium bowl, beat together the eggs. Mix in the buttermilk, vanilla extract, coffee extract, and butter.
In another medium bowl, sift together the flour, sugar, baking powder, and salt. Use a wooden spoon or spatula to gently fold into the liquid ingredients until just incorporated. Allow to rest while you heat the pan.
Place a large steel skillet over medium heat. Set aside a damp towel. Once heated, place briefly on the wet towel (do not do this if using cast iron or enamel) and place back on burner over low heat. Lightly grease with oil, spread with a towel, pour 1/4 cup of the batter in prepared skillet, and cover. Once golden on bottom and bubbles begin to form on top, about 4 minutes, flip to other side. Continue to cook until golden, another 1-2 minutes. Repeat with remaining batter.