Make dough: Sift together flour, confectioners' sugar, baking powder, and salt in a large bowl. Sift again. Transfer to the bowl of a food processor. Add butter; pulse until largest pieces are the size of peas. Add egg yolks and sour cream; pulse until dough just begins to come together. If dough is too dry, add ice water, 1 tablespoon at a time, and pulse.

Knead dough and form into disk; refrigerate: Transfer dough to a lightly floured surface and knead until dough comes together. Form into a disk and wrap in plastic. Refrigerate until firm but pliable, at least 1 hour.

Preheat oven, prepare pan, roll out dough: Preheat oven to 375°F with rack in center. Lightly butter a 10-inch round springform pan. On a lightly floured surface, roll out dough into a 15-inch circle, about ⅛ inch thick.

Fit dough into pan and freeze: Fit dough into bottom and up side of pan. With a paring knife, trim dough to about ½ inch below the rim. Crimp edges with the tines of a fork. Freeze until firm, 10 minutes.

Blind bake crust: Line dough with parchment. Fill with dried beans or pie weights; bake until crust is firm and dry, 18 to 20 minutes. Remove parchment and beans; let cool completely. Reduce oven temperature to 350°F.

Make filling: In the bowl of an electric mixer fitted with the paddle attachment, beat together eggs and egg white on medium speed until thick and pale, about 2 minutes. Gradually beat in granulated sugar to combine. Add farmer cheese, sour cream, lemon and orange zests, raisins, and vanilla; mix until fully combined. Transfer filling to cooled crust.

Bake and cool cheesecake: Bake cheesecake until set at edges but still slightly wobbly in center, 50 to 55 minutes. (If it is browning too quickly during baking, tent edges of crust with foil.) Transfer to wire rack; let cool completely. Refrigerate until cold, at least 8 hours; serve.