3 cups cake flour
1 teaspoon ground cinnamon
1 1/4 teaspoon baking soda
1/2 teaspoon kosher salt
3/4 cup (6-ounces) unsalted butter at room temperature
1 cup packed light brown sugar
1/2 cup granulated sugar
3 extra large eggs at room temperature
1 Tablespoon grated fresh ginger
1 cup plus 2 Tablespoons buttermilk at room temperature
1 cup finely chopped crystallized ginger

For the Frosting
2 (8-ounce) packages cream cheese, softened
1/2 cup (4-ounces) unsalted butter at room temperature
3/4 cup packed light brown sugar
2/3 cup confectioners' sugar
1/2 teaspoon ground cinnamon
1/4 teaspoon ground ginger
1/4 teaspoon pure vanilla extract
1/4 teaspoon lemon zest
1/2 cup finely chopped crystallized ginger, divided

Accompaniment
Cinnamon Ice Cream