In stand mixer bowl, add 1 cup flour, yeast, sugar and salt; mix well. In saucepan or microwave-safe dish, heat water, sour cream and butter to 120-130°F (butter does not need to melt). Add to flour mixture. Using a paddle attachment, blend on medium speed for 2 to 3 minutes. Add eggs and vanilla; beat 1 minute.
Switch to dough hook attachment. Gradually stir in enough of the remaining 2 cups of flour to make a firm dough. Knead until smooth and elastic, about 5 to 7 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.)
Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 30 to 40 minutes.
Prepare filling: cream together cream cheese, egg, sugar, and salt.
Punch down dough and divide in half. On a lightly floured surface, roll each half to a 12x17-inch rectangle. Spread half of filling lengthwise over center third of dough. Top with approximately half of pie filling. (Save a few cherries from filling to decorate coffee cake after it is baked.) On each long side, cut 1-inch wide strips, 2 inches long. Starting at one end, fold strips at an angle across filling, alternately from side to side. Place coffee cake on greased baking sheet. Cover; let rise until indentation remains after lightly touching the side of the coffee cake, approximately 30 minutes.
Preheat oven to 350°F.
Bake in preheated oven 30 to 35 minutes. Cool on wire rack.
Prepare icing: Mix water and powdered sugar together. Add more/less powdered sugar to achieve desired consistency. Drizzle cooled coffee cake with icing; place a few cherries on small lattice openings to decorate.