Position oven rack 1/3 up from the bottom of the oven; preheat oven t 325°.
You will need a 10 x 4 inch tube pan; it must NOT be a nonstick pan and it must be the kind made in two pieces—the bottom and tube in one piece and the sides in a separatepiece; do NOT butter the pan.
On a board, with a heavy knife, cut the chocolate into small pieces; aim for pieces ¼ inch in diameter; do not leave any pieces larger than ¼ inch, because this is a very light cake and larger pieces might sink to the bottom; set aside.
In a large mixing bowl, sift together the flour, 1 ¼ cup sugar, instant coffee, baking powder, and salt.
With a rubber spatula make a wide well in the middle of the dry ingredients.
Add, in the following order, without mixing, the oil, egg yolks, Kahula, water, and vanilla.
With a large strong wire whisk, beat the ingredients until smooth.
Remove the whisk and with a rubber spatula stir/fold in the chopped chocolate; set aside.
In the large bowl of an electric mixer, beat the whites until foamy, add the cream of tartar, and beat at high speed until the whites hold a soft shape.
Decrease speed to medium and gradually add the remaining ½ cup sugar.
Then, on high speed again, beat until the whites hold a straight and stiff peak when the beaters are withdrawn.
For the recipe the whites should be stiffer than for most; when the whites are firm, beat for 1 minute more to be sure.
That should make them just right; more beating than that might make them too dry.
Use a large-size rubber spatula—in three additions, fold about ¾ of the yolk mixture into the whites, without being too thorough (without being even a bit thorough).
Then fold the whites into the remaining yolk mixture, this time being thorough enough to just barely incorporate the mixtures.
Gently pour the batter into the cake pan and gently smooth the top if necessary.
Bake for 1 hour and 10-15 minutes, until the top springs back when pressed gently with a fingertip; the top will crack during baking—it is ok.
Immediately turn the pan over and hang it upside down over the neck of a narrow bottle (even if your pan has a raised tube in the middle or three little feet on the sides, they probably will not raise the cake enough to keep it off the counter top).
When the cake is completely cool, remove it from the pan as follows—you will need a sharp knife with a firm blade about 6 inches long; insert knife between the cake and the rim in order not to cut into the cake.
With short up and down motions, saw all around the cake, continuing to press the blade against the side of the pan; then cut around the tube.
Remove the sides of the pan by pushing up on the bottom of the pan; then, carefully cut the bottom of the cake away from the pan, still pressing against the pan.
Cover the cake with a wide, flat cake plate, turn the cake and plate over, and lift off the bottom of the pan, leaving the cake upside down.
Sprinkle with powdered sugar through a fine strainer.
Use a serrated knife and a sawing motion to slice the cake without squashing it.