In a large bowl, combine 1 1/2 cups flour, sugar, cinnamon, salt, nutmeg and yeast.
Heat milk, water and butter until hot to touch (125 to 130F). Gradually add to dry ingredients. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionall. With spoon, stir in enough additional flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 minutes. Cover, let rest on board 20 minutes.
Punch dough down, turn out onto lightly floured surface. Knead in dates. Divide dough into 18 equal pieces, form into smooth balls. Place balls on greased baking sheets, 2 inches apart, or in 2 greased 8-inch square baking pans. Cover, let rise in warm, draft-free place until doubled in size, about
30 minutes.
Brush with egg white mixture. Bake at 375F for 20 minutes. Remove from pans and cool on wire racks. Drizzle frosting on rolls to make a cross.
Vanilla frosting: Stir together 1 1/2 cups icing sugar, 1 to 2 tablespoons milk and 1/2 teaspoon vanilla extract.
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