Mix 2 cups of the flour, 1/3 cup sugar, the salt, and yeast in a large bowl. Heat shortening, water and milk to 125 to 130 degrees (shortening may not be melted); stir into flour mixture. Mix in egg; beat until smooth, about 2 minutes. Mix in enough of the remaining flour to make dough easy to handle. Turn dough onto lightly floured surface; knead until smooth, 3-5 minutes. Cover and let rest 10 minutes.
Meanwhile, make cream cheese filling: Mix cream cheese, 1/4 cup sugar, 3 T. flour and egg yolk until smooth and fluffy. Set aside.
Grease two 9-inch round pans. Mix cranberry sauce with lemon peel or almond extract (your choice); reserve.
Divide dough into halves; roll each half into 15-inch circle. Fold into fourths; place in pan with point in center. Unfold; press dough against side, allowing edge to hang over edge of pan. Spread half of the cream cheese filling over dough in each pan; top each with half of the cranberry sauce. Make cuts at 1-inch intervals to about 1/2-inch above filling around outside edge of dough. Twist strips and fold over sauce.
Beat egg white with hand beater until foamy; brush over dough. Sprinkle each cake with 1/4 cup almonds and 2 T. sugar. (At this point, coffee cakes can be covered and refrigerated up to 24 hours; rising time may be slightly longer.) Cover and let rise 45 minutes.
Heat oven to 375 degrees. Bake until golden brown, 30-35 minutes; cool slightly.