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PdfPreheat oven to 300°F. Whirl shortbread in food processor until sandy and no lumps remain. Press crumbs into bottom of ungreased 8" round pan with 3" sides (I like the pan with the removable bottom that Fat Daddio makes).
Beat yolks with sugar and vanilla paste (or seeds) until light and sugar has mostly dissolved (rub a little between finger and thumb to test). Mix in the melted butter, then flour and salt, then cream cheese. Beat until no lumps remain. Slowly add milk and stir until mixture is smooth and homogeneous.
Beat egg whites until stiff but not dry. Fold gently into cream cheese mixture until no large pockets of whites remain. Pour batter into prepared pan.
Bake for 1 hour (no peeking!), then turn off oven and prop open door with wooden spoon. Let cake stand in warm oven for one hour. Cool on countertop. Room temperature or slightly warm, this cheesecake has a wonderful souffle-like texture. Refrigerate for at least 5 hours for the traditional, dense cheesecake texture.