In an electric stand mixer, fitted with the paddle attachment, combine 1 ½ cups of flour, sugar, salt, cinnamon, allspice, and yeast.
In a small saucepan, heat milk and butter until warm and all butter melts (about 125°F).
Add milk and butter mixture to the flour mixture. Add eggs and beat at low speed until all ingredients are combined. Switch to the hook attachment of your mixer and add the rest of the flour to the mixture. Add raisins and pineapple. Beat for 5 minutes at medium speed until the dough cleanly pulls apart from the bowl.
Place the dough in a lightly greased bowl and cover with plastic wrap and a kitchen towel. Place in a warm place and allow the dough to rise until doubled in size, about 45 minutes to 1 hour depending on the temperature of your kitchen.
Place the dough in a clean surface and punch down the dough to remove all air bubbles. Evenly divide the dough into 15 pieces. Shape the pieces of dough into balls. Place the dough balls in a baking sheet lined with parchment paper. Cover with plastic wrap and allow the dough to rise until doubled in size. About 30 minutes.
Preheat oven to 375°F. Brush the buns with egg white. Bake for 20 – 25 minutes or until golden brown. Remove from oven and cool slightly.
While the buns are cooling down, prepare the frosting. In a small bowl, combine all the ingredients until smooth. Adjust the consistency of the frosting adding additional milk or powdered sugar if needed.
Using a piping bag, decorate the buns making a cross on each roll.