Preheat oven to 350 degrees. Pulse cookies in a food processor until crumbs form. (You should have 1 cup.)Process with pistachios, sugar and cheese until fine crumbs form. Add butter and process until the mixture holds together.
Press crumb mixture evenly into bottom and up sides of a 9-inch fluted tart pan with a removable bottom. Refrigerate for 15 minutes. Bake until golden brown, 17 to 20 minutes. Transfer to a wire rack, and let cool.
In the bowl of an electric mixer fitted with the paddle attachment, beat the cream cheese on medium speed until fluffy (about 3 minutes), scraping down sides as needed. In a large bowl, whisk together sugar and flour. With mixer on low speed, gradually add sugar mixture to cream cheese; mix until smooth. Add sour cream, vanilla and cardamom; mix until smooth. Add eggs, one at a time, beating until just combined; do not over mix.
Pour cream cheese filling into prepared pan. Set pan inside a large, shallow roasting pan. Carefully ladle boiling water into roasting pan to reach halfway up sides of springform pan. Bake 45 minutes; reduce oven temperature to 325 degrees. Continue baking until cake is set but still slightly wobbly in the center, about 30 minutes more. Turn off oven; leave cake in oven with door slightly ajar, 1 hour. Transfer pan to a wire rack; let cake cool completely. Sprinkle top of cake with tea powder. Refrigerate, uncovered, at least 6 hours or overnight. Before unmolding, run a knife around the edge of the cake.