Put butter, eggs, yolks, granulated sugar, salt, vanilla, zests, Cognac, and sour cream in the bowl of an electric mixer fitted with the whisk attachment; beat on medium speed until pale and thick, 8 to 10 minutes. Reduce speed to low; gradually add enough flour to form a fairly stiff dough. Turn out dough onto a floured work surface; knead until dough blisters, becomes elastic, and can be handled easily, 6 to 8 minutes, adding flour if needed.
Divide dough into 4 pieces. Keep dough under an inverted bowl to prevent it from drying out. Working with 1 piece at a time, roll out dough to 1/8 inch thick. If dough becomes too elastic while rolling, cover with plastic, and let rest 15 minutes. Cut out leaves with a leaf-shape cookie cutter; transfer to a tray lined with parchment paper. Repeat with remaining dough, layering leaves between sheets of parchment paper. Collect all scraps, and let rest 20 minutes before rerolling.
Heat oil in a medium-heavy saucepan until it registers 375 degrees on a deep-fry thermometer. Stretch leaves slightly so they will curl while frying. Fry in batches of 12, turning occasionally, until pale golden brown, about 3 minutes. Transfer to baking sheets lined with paper towels to drain and cool. Sprinkle with confectioners' sugar. Store in airtight containers at room temperature up to 2 days.