Mound the flour in a large mixing bowl. Combine the salt and 1 teaspoon of sugar and place them at 1 edge of the bowl. Put the yeast on the other side. (Do not mix the yeast and the salt yet; the salt will soak up the moisture in the yeast, killing it.) Stir first the eggs, and then the beer into the flour. Mix in 3 1/2 tablespoons water, incorporating the sugar, salt and yeast as you go and working until the batter is smooth. Cover the batter with plastic and set it aside in the refrigerator to relax for at least 1 hour.

Whip the egg whites until they hold soft peaks. Fold the whipped whites into the batter (this makes for lighter beignet).

Heat about 2-inches of oil in a deep pot over medium-high heat until the oil reaches 350 degrees F.

Slice the apple into 8 (1/2-inch) thick slices. Mix the remaining 1 teaspoon of sugar with the cinnamon. Dust the apple slices with cinnamon-sugar. Working in batches of 2 or 3, dip slices of apple into the batter then carefully drop the beignet into the hot oil. Fry the beignet until crisp and uniformly golden brown, about 4 minutes per side then drain on a plate lined with paper towels. Allow the beignet to cool for a few minutes then sprinkle with confectioners' sugar and serve.