In a medium bowl, combine the 1� cup all purpose flour, baking powder, baking soda, salt, sugar and yeast.
In a small bowl, whisk together the egg, buttermilk and vanilla.
Add the egg mixture to the flour mixture and stir until the flour is incorporated. The dough will be sticky. Put the dough to a lightly floured surface and knead dough until smooth and slightly sticky the touch (try not to over knead), adding more flour if necessary. Transfer the dough to a clean medium bowl dusted with a little flour. Cover with plastic wrap and let rest until doubled in size, about 2 hours.
Punch down dough and turn onto a lightly floured surface. Using your hands, pat down dough and form into an oval shape, about �-inch thick. Cut into 1 1/2-inch squares.
Preheat oil for frying in heavy skillet ? oil should be 3/4-inch deep for frying.
When oil registers 365 degrees F, fry pieces of dough in batches (don?t overcrowd the pan) for 1 minute on each side or until evenly golden brown. Transfer beignets to a tray lined with paper towel to drain. Dust with cinnamon and/or icing sugar. Serve.
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