Oh, here's a "yeastless" beignet. Not tried and true...
but you still need to deep-fry it (which is almost as potentially disaster ridden for me). Here it is, anyway:
Beinets Or French Fritters
RecipeView.com
4 Eggs
6 Tbl water
1 Tsp Vanilla
1 Tbl Butter
Confectioner's sugar
6 Tbl All-purpose flour
Heat deep fat to 370 degrees F. Combine water, butter and flour in a saucepan and boil, stirring constantly, over low heat for about 5 minutes. Remove pan from heat and beat in eggs, one at a time.
Beat batter for about 3 minutes after the addition of each egg. Add vanilla and drop the batter from a teaspoon into the hot fat. Cook until golden; drain and dust with confectioner's sugar.
Note: If you use butter or part butter for frying, start frying with the fat at 330 degrees and let the heat rise over a 7 minute period to 360. Be sure to bring the heat of the fat DOWN to 330 again between cookings.
SOURCE; JOY OF COOKING; author Irma S. Rombauer and Marion Rombauer Becker