For filling: Place pineapple in a heavy saucepan. Add sugar and lemon juice.
Bring to a simmer. Reduce heat and cook, uncovered, until liquid almost evaporates,
about 30 minutes. Stir in vanilla extract. Cool.
For cake: Combine 1 cup of flour, sugar, yeast and salt in a large bowl.
Heat milk and butter in a saucepan or microwave until mixture reaches 110 degrees
Using a large whisk, add hot milk-butter mixture and vanilla to flour mixture;
beat until well combined. Add eggs, one at a time, blending well after each. Add
remaining flour, 1/2 cup at a time, to make a soft dough that just cleans sides
of bowl. Switch to wooden spoon when dough becomes too thick for a whisk.
Cover bowl with plastic wrap and refrigerate for 1 hour. Turn chilled dough out
onto a floured surface. Knead gently until smooth but still soft. Dust with 1 tablespoon
of flour at a time to keep from sticking; do not over-flour. Place dough in a greased
container, turning once to grease top. Cover and let rise at warm room temperature
for 1 1/2 hours.
Meanwhile, prepare the cheese filling and crumb topping.
Cheese filling: Beat the cream cheese, sugar, eggs and vanilla extract in the
bowl of electric mixer until smooth. Refrigerate until needed.
Topping: Combine the flour, sugar, cinnamon and butter in food processor bowl;
pulse until crumbly.
After dough has risen for 1 hour, preheat oven to 350 degrees F. Line a 12 x
18 x 1-inch baking sheet with parchment. Rub with butter or shortening.
Turn dough onto a lightly floured board and divide in half.
Roll out one half of the dough to a 12 x 18-inch rectangle. Fit into pan and
press up along the sides. Spread cheese filling evenly over dough. Spread pineapple
filling over cream cheese filling.
Roll out remaining dough to a 12 x 18-inch rectangle. Place on top of fruit filling
and tuck in sides to contain filling. Crimp edges. Sprinkle crumbs on top and set
cake aside for 15 minutes.
Bake for 35 to 40 minutes, until golden brown and firm to the touch.