Melt butter in milk and cool to lukewarm. Place water in a warm large mixing bowl, sprinkle in yeast, and stir until dissolved; add milk mixture and sugar. By hand, beat 2 1/2 cups flour in until smooth; mix in eggs, salt, and spices. Mix in remaining flour, adding a little extra, if needed, to form a soft but manageable dough. Knead lightly 1 minute on a floured pastry cloth; shape into a ball, place in a greased large bowl, cover, and let rise in a warm, draft-free spot until doubled in bulk, about 1 hour.
Punch dough down, roll 1/2-inch thick on pastry cloth, using a floured, stockinette-covered rolling pin. Cut with a floured doughnut cutter and place 1 1/2-inches apart on un-greased baking sheets. Reroll and cut scraps. Cover with cloth and let double in bulk.
Meanwhile, begin heating fat in a deep fat fryer. When doughnuts have risen and fat has reached 375 degrees F, ease 4 doughnuts into fat, 1 at a time. Fry about 2 minutes until golden brown all over, using tongs to turn. Drain on paper toweling.
While doughnuts are warm, roll in topping.
Jelly Doughnuts: Prepare as directed, but roll dough 1/4-inch thick instead of 1/2-inch. Cut in 2 1/2-inch rounds and put 1 teaspoonful tart jelly in the center of 1/2 the rounds. Top with remaining rounds, moisten touching edges slightly, and pinch to seal. Let rise, then fry as directed. Roll in confectioners' sugar while still warm.
Crullers: Prepare as directed, but instead of cutting into doughnuts, cut in strips 8-inches long and 1/2 to 3/4-inch wide; let rise, then twist strips several times and pinch ends. Fry at once and roll in topping while still warm.
Never fry more than 4 doughnuts at a time and keep fat as near to 375 degrees F as possible; if too hot, doughnuts will brown before they cook inside.
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