Preheat oven to 400 degrees. Mix flour, sugar, baking powder, baking soda, salt, and cardamom in large bowl. Add zest.
Cut cold butter into small cubes and add to flour mixture. Rub flour and butter between your fingers until mixture resembles a coarse meal.
Add dried strawberries and white chocolate chips. Slowly add buttermilk and vanilla.
Turn dough onto clean, floured surface. Knead until dough is no longer sticky.
Pat dough into 1-inch tall circle or rectangle. Cut into eight equal pieces.
Place on parchment-lined baking sheet - reshape if necessary.
In a small bowl whisk egg and half & half. Brush egg mixture over scones.
Bake 20-25 minutes, rotating ten minutes into baking time. Let cool completely.
In a medium bowl, whisk powdered sugar, milk, and jam. If too thick to drizzle, add more milk in very small increments. If too thin, add powdered sugar.
Drizzle icing over scones. Enjoy immediately or let sit. Cover to serve next day.