How to Make It
In a bowl, whisk the flour with the baking soda, cinnamon, ground ginger, nutmeg, cardamom and salt until evenly combined. In the bowl of a stand mixer fitted with the paddle, combine the butter and 2 cups of the granulated sugar with the grated ginger, orange zest and vanilla. Beat at medium speed until light and fluffy, about 3 minutes. Add the eggs 1 at a time and beat until incorporated. Beat in the molasses, then add the dry ingredients and beat at low speed until incorporated. Scrape the dough into a large bowl, cover with plastic wrap and refrigerate for at least 8 hours or overnight.
In a small saucepan, cook the butter with the vanilla bean and seeds over moderately high heat, stirring occasionally, until the butter begins to brown and smell nutty, about 4 minutes. Pour into a metal bowl set over an ice bath, making sure to scrape the browned solids from the bottom of the pan into the bowl. Add the salt and stir the butter until cooled and beginning to solidify. Discard the vanilla bean and let the butter stand in the ice bath until completely solid. Remove from the ice bath.
In the bowl of a stand mixer fitted with the paddle, beat the cream cheese at medium speed until light and fluffy. Add the brown butter and confectioners’ sugar and beat at low speed until smooth. Increase the speed to high and beat until fluffy, about 2 minutes. Scrape the frosting into a medium bowl, cover with plastic wrap and refrigerate for at least 1 hour.
Preheat the oven to 350°. Line 2 large rimmed baking sheets with parchment paper. Place the remaining 1/2 cup of granulated sugar in a small bowl. Working in 2 batches, using a 1-ounce ice cream scoop or two tablespoons, portion the dough into 1-inch balls. Roll the balls in the sugar and arrange on the prepared sheets at least 2 inches apart. Using the flat bottom of a glass or measuring cup, gently flatten each ball into a thick disk. Bake the cookies for 14 minutes, until set at the edges; rotate the baking sheets from top to bottom and front to back halfway through baking. Let the cookies cool for 10 minutes on the baking sheet, then transfer to a rack and let cool completely.
Stir the frosting until spreadable. Dollop 1 heaping tablespoon on one side of half the cookies, then sandwich with the remaining cookies.