In a medium mixing bowl stir together 1 cup of the flour and the yeast; set aside. In a small saucepan heat and stir evaporated milk, water, granulated sugar, butter, and salt just until warm (120 degree F to 130 degree F) and butter is almost melted. Add milk mixture to flour mixture; add egg. Beat with an electric mixer on low to medium speed for 30 seconds, scraping sides of bowl constantly. Beat on high speed for 3 minutes. Using a wooden spoon, stir in as much of the remaining flour as you can.
Turn dough out onto a lightly floured surface. Knead in enough of the remaining flour to make a moderately stiff dough that is smooth and elastic (6 to 8 minutes total). Shape into a ball. Place in a lightly greased bowl, turning once to grease surface. Cover and let rise in a warm place until double in size (about 1 hour). Punch dough down. Turn out onto a lightly floured surface. Divide into 2 portions, with three-fourths of the dough in larger portion. Cover and let rest for 10 minutes.
Grease a 10-inch springform pan with a removable bottom; set aside. In a small bowl beat together cream cheese, powdered sugar, and vanilla until smooth. Roll larger portion of dough into an 11-inch circle. Fit into the prepared pan, covering bottom and 1/2 inch up sides. Spread cream cheese mixture over bottom; top with an even layer of spreadable fruit.
Roll remaining dough into a 9x5-inch rectangle. Cut into five 9x1-inch strips. Twist each strip 4 times. Place 3 strips on spreadable fruit at 2-inch intervals, stretching strips slightly if necessary. Place remaining strips horizontally across strips already in place. Press ends into sides of crust, trimming if necessary. Cover and let rise in a warm place until nearly double in size (about 30 minutes).
Bake in a 350 degree F oven about 35 minutes or until crust is golden brown. (If necessary, loosely cover with foil the last 10 minutes of baking to prevent overbrowning.) Cool on a wire rack about 45 minutes. Makes 10 servings.