I don't know how Irish it is, but I was told it was when I got the recipe, and it is delicious (and much more impressive then green sugar cookies). Don't be intimidated by the old-fashioned two-hour steaming, it's not difficult, just sounds so.
Melt the chocolate and butter together; set aside.
Beat the egg whites until foamy, gradually add 1/2 cup sugar (still beating), then beat to soft peaks; set aside.
Beat the egg yolks, gradually adding the remaining sugar.
Continue beating until the mixture has about tripled in volume, and the sugar is dissolved. The yolks should look light yellow.
Add the chocolate mix to the yolks, beating until blended.
Then add the flour, beating on low speed until thoroughly mixed.
Fold the mixture into the egg whites.
When completely mixed, pour into a very well greased 7 cup pudding basin, or a bowl suitable for use on the stove.
If using the bowl, construct a lid as follows: Cut a piece of wax paper large enough to cover the bowl, with some excess for folding. Fold a one inch pleat in the middle of the wax paper. Do the same with a piece of aluminum foil. Cover the bowl with the wax paper, then with the foil, lining up the pleats. Secure with kitchen twine; cut off any excess.
You may wish to construct a lifter out of twine, or you can use two spatulas to lift the pudding.
Pour about two inches of water into a pot large enough to fit your pudding basin. Place the basin inside and cover the pot.
Keep the water in the pot boiling for about 1 1/2 to 2 hours. (You will need to add more boiling water from the kettle from time to time.).
The pudding will be firm and cakelike on top when it is finished. If you are not sure, boil it longer, it can't be overdone.
Once it is ready, let it cool for a few minutes in the basin, then turn it out on a plate.
You may serve it warm or let it "age" in an airtight container, which will richen the flavor.