Preheat oil for frying to about 350°F. Oil should be at least 2-inches deep, if a deep fat fryer isn't available an electric skillet works well for frying beignets.
Combine 1 cup flour, undissolved yeast, sugar, salt and baking powder in a large bowl. Heat buttermilk and water to very warm (120°F to 130°F). Mixture may look curdled. Add to flour mixture and mix until well combined. Add remaining 1 cup flour and mix well. Dough will be sticky.
Place dough on very generously floured surface. Roll dough to a 9 x 15-inch rectangle, adding more flour as needed. Cut into squares, 4 x 6.
Fry 3 to 4 beignets at a time, turning occasionally until well browned, about 2 to 3 minutes. Remove from oil and drain on paper towels. Cool a few minutes, then generously sprinkle with powdered sugar. Serve immediately.