Combine flour and brown sugar; stir well, and set aside.
Dissolve yeast in water, stirring well; let stand 5 minutes.
Combine next 4 ingredients in a large bowl; mix well. Cool to lukewarm (105° to 115°). Add dissolved yeast; mix well. Gradually stir in enough flour mixture to make a soft dough.
Place dough in a greased bowl, turning to grease top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Punch dough down; turn out onto a lightly floured surface, and let rest 5 minutes. Knead butter into dough, 2 tablespoons at a time. Roll dough to 1/2-inch thickness; cut with a 1 1/2-inch biscuit cutter. Place doughnuts on greased baking sheets. Cover and repeat rising procedure 1 hour or until doubled in bulk.
Drop doughnuts, a few at a time, into hot oil (340°). Fry until golden brown, turning once. Drain; sprinkle with powdered sugar.