Prepare two 13” x 9” baking pans by lining them with parchment paper, including up the sides.
Preheat the oven to 395 degrees F. (~200 degrees C).
In a small bowl, mix 1 C. of flour, baking powder, and salt.
In a medium sauce pot, place water and 125g of butter. Cook on medium heat until the butter melts and the mixture boils.
Add the flour mixture to the butter, and mix vigorously with a wooden spoon. The dough will form into a smooth ball, but keep cooking and mixing this ball for about a minute.
Transfer the dough to a mixing bowl (or stand mixer), and begin beating it with an electric mixer for about a minute to cool it down.
While beating on high, add the eggs ONE AT A TIME, beating for about 30 seconds between eggs. The dough will look like wet crumbles at first, but around egg 4 or 5 it will quickly turn into a thick smooth dough.
Divide the dough between the two baking pans.
Carefully spread the dough out along the bottom of the baking pans - this will feel like working with glue or putty. Be patient, the layer will be very thin on the bottom of the pans. It’s best to use a metallic object to spread the dough, like the back of a spoon.
Place both pans in the oven and bake for 25 minutes.
Turn out the cakes from the pans, remove the parchment paper, and place them on wire racks to cool. The cakes will look like a mountain range, hence the name “Karpatka”, which is inspired by the Polish name for the Carpathian Mountain range.