Egg wash: Combine the yolks, whole egg, and milk in a small mixing bowl and whip with a hand whisk until well combined.
Preheat the oven to 400 degrees F (204 degrees C). Remove the puff pastry from the refrigerator. If you are only making 1 thing at a time, return the rest of the puff pastry to the refrigerator.
Cheese twists: Place a piece of puff pastry on a lightly floured work surface and pat it into a rectangle. Use a rolling pin to roll the puff pastry into a 12 by 20-inch rectangle about 1/8-inch thick. Roll the dough thinly because it will rise in the oven. Flour the dough and table as needed to keep the dough from sticking to the table or the rolling pin. Place the dough on your work surface with a long side facing you. Use a pastry brush to coat the surface of the rectangle with some egg wash. Liberally sprinkle the Parmesan cheese over the rectangle, followed by the salt and pepper. Use a sharp paring knife to cut the rectangle into 1-inch-wide strips from top to bottom. Flip each strip so that the cheese is on the bottom. Twist each strip by rolling each end in opposite directions. Always remember to twist so that the topping faces out --that way you can see how they are flavored. Place the strips on a parchment paper-covered baking sheet and bake until well risen and golden brown, about 20 minutes. Cool completely on a wire rack before serving.
Anchovy puffs: Place a piece of puff pastry on a lightly floured work surface and pat it into a rectangle. Roll the dough into a 10 by 12-inch rectangle with the long side facing you and cut it in half from top to bottom. Use a pastry brush to coat 1 piece of the dough with egg wash. Lay the anchovy fillets spaced about 1-inch apart from top to bottom on the egg-washed dough. Place the other rolled-out dough half on top of the anchovies and mark each anchovy by pressing the dough on either side of each fillet. Use a sharp paring knife to cut between each puff pastry-covered fillet. Next, cut the filled strips in half from top to bottom to make small anchovy packets. Use a knife to score the top of the dough at a diagonal. Place on a parchment paper-covered baking sheet and brush with more egg wash. Bake until well risen and golden brown, about 20 minutes. Cool completely on a wire rack before serving.
Olive puffs: Place a piece of puff pastry on a lightly floured work surface and pat it into a rectangle. Use a rolling pin to roll the dough into a 10 by 12-inch rectangle and repeat the procedure of making anchovy strips using olives instead. There is no need to cut these in half. Just cut between the olives to make small packages. Baking and cooling is the same.
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