In a mixing bowl, combine the all-purpose flour, pastry flour, granulated sugar, salt, and instant yeast. Mix well.
Add the cold, cubed butter into the flour mixture and use a pastry cutter or your fingers to blend it until it resembles coarse crumbs.
In a separate bowl, combine the warm milk, egg, and vanilla extract. Mix until combined.
Gradually pour the wet ingredients into the dry ingredients, mixing until a dough forms.
Turn the dough onto a floured surface and knead gently until just smooth. Be careful not to over-knead.
Wrap the dough in plastic wrap and refrigerate for at least 1 hour.
After chilling, roll out the dough into a rectangle about ½ inch thick. Fold it into thirds (like a letter), then roll it out again. Repeat this process two more times for layers.
Roll the dough out to about 1 inch thick, then use a round cutter (about 3 inches in diameter) to cut out circles. Use a smaller cutter (about 1 inch in diameter) to cut out the centers, creating a donut shape.
Place the shaped cronuts on a baking sheet lined with parchment paper and let them rise for about 30 minutes.
Meanwhile, heat oil to 350°F (175°C) in a deep fryer or heavy-bottomed pot.
Fry the cronuts in batches for about 3-4 minutes on each side or until golden brown. Remove with a slotted spoon and drain on paper towels.
While still warm, roll the cronuts in a mixture of powdered sugar and cinnamon (if using).
Allow to cool on a wire rack before serving.