In an electric stand mixer, fitted with the hook attachment, combine flour, sugar, yeast, cinnamon, ginger, cardamom, and salt.
In a small saucepan, heat almond milk and butter until warm and all butter melts (about 125°F).
Add milk and butter mixture to the flour mixture. Add applesauce and beat at low speed until all ingredients are combined. Beat for 10 minutes at medium speed until the dough cleanly pulls apart from the bowl. Add raisins and pineapple.
Place the dough in a lightly greased bowl and cover with a kitchen towel. Place in a warm place and allow the dough to rise until doubled in size, about 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 12 pieces. Shape the pieces of dough into balls. Place the dough balls in a baking sheet lined with parchment paper. Cover with a kitchen towel and allow the dough to rise until doubled in size, about 1 hour.
Preheat oven to 400°F.
Prepare the topping. In a small bowl, combine flour, sugar, and water and stir until a smooth paste is formed. Place the mixture in a pastry bag, pipe crosses on top of each bun.
Bake for 20-24 minutes until golden brown. While the buns are baking, heat in a small saucepan the apricot jam until it liquefies. Remove the buns from the oven and immediately brush jam over them. Serve hot.
Additional Tips: Serve buns with apricot jam or orange marmalade.