In stand mixer bowl, add 1 cup flour, yeast, sugar; mix well. In saucepan or microwave-safe dish, heat sour cream and butter to 120-130°F (butter does not need to melt). Add to flour mixture. Using a paddle attachment, beat on medium speed for 4 minutes. Add eggs and vanilla; beat 1 minute.
Switch to dough hook attachment. Gradually stir in enough remaining 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 1 hour.
Prepare pan: grease 9x13-inch cake pan; set aside.
Prepare filling: Cream all ingredients together; set aside.
Turn dough onto lightly floured surface; punch down to remove air bubbles. Divide dough into 2 unequal pieces (one is 1/3 of dough, and one is 2/3 of dough). Roll out larger piece on a floured surface to a 10x14-inch rectangle. Place in prepared pan; pressing dough up sides.
Spread filling evenly over dough.
Roll out remaining dough piece to a 5x12-inch strip. Cut into five 1x12-inch strips. Lay strips lengthwise over filling. Fold down sides of dough to hold strips in place. Cover; let rise until indentation remains after touching.
Preheat oven to 350°F.
Prepare icing: In a small bowl, add pineapple juice to powdered sugar and stir together until smooth. If the icing is too thin, add more powdered sugar; too thick, add more pineapple juice.
After rising, bake for 30 to 35 minutes. Cool in pan. Drizzle with icing.