In a medium bowl, add the flour, cardamom and salt, and whisk to combine. Heat oven to 350 degrees and line two baking sheets with parchment paper. In a large bowl, beat together sugar, butter, eggs and vanilla, until fluffy. Create a well in the center, and pour in the water and milk. Wrap in plastic and refrigerate 1 hour. Measure 1 rounded tablespoon of dough; Whisk first 4 ingredients in a medium bowl. Reduce speed and beat in flour mixture. Mix on the lowest setting until just combined and beginning to form a dough, 1 to 2 minutes. Working inside the bowl, give the dough a couple.
In a medium bowl, add the flour, cardamom and salt, and whisk to combine. Continue on low to knead dough, about 2 minutes. Working inside the bowl, give the dough a couple. Knead the dough between floured hands until malleable. Mix on low speed until a tight, smooth dough comes together around the hook, about 5 minutes. Remove the hook and cover the bowl with a damp towel. Arrange racks in lower and upper thirds of oven; Reduce speed and beat in flour mixture. Set aside for 10 minutes. Measure 1 rounded tablespoon of dough; It should go from shaggy and coarse to smooth and shiny.
