For the dough, combine all of the ingredients to make a soft dough. Place the dough on a baking sheet and pat it into a 10” x 14” rectangle. Place on a floured baking sheet, cover and refrigerate while you prepare the butter.
For the butter, combine all of the ingredients listed just until smooth, either by hand or at slow speed with a mixer (you don’t want to beat air into it; mix just enough to make the mixture homogenous). Line a baking sheet with plastic and spread the butter into a rectangle 9” wide by 10” long. Wrap and chill for 20 minutes.
To assemble, the dough and butter should be the same consistency: flexible but firm.
Flour your work surface and turn the dough out onto it, with the long edge facing you. Unwrap the butter and place it on the left end of the dough, leaving a ½” border of dough around the sides and a third of the dough uncovered. Lightly wet the outside edges of the dough with your fingers. Fold the uncovered section of the dough over the butter and line up the edges, pinching them closed. Fold the exposed butter and dough over to make a 3-layer packet. Tap the top of the packet lightly with your rolling pin, and roll the packet out to 24” long.
Fold the packet in thirds once more, like a business letter. If the dough is becoming soft, place on a parchment lined baking sheet, cover and refrigerate for 30 to 45 minutes before continuing. If the dough is still firm and cool to the touch, roll it out and fold it once more before chilling (this would count as 3 folds).
After chilling, roll the dough and fold once more. Wrap and chill the dough for at least 4 hours and preferably overnight before using. You can also divide the dough and freeze it if you want to make a smaller batch and save some for later.
To shape the Danish, preheat the oven to 400°F.
Divide the dough in half. Roll the dough out to about a 13” square. With a sharp knife, trim the edges to be straight, leaving a 12” square piece of dough. Cut the dough into nine 4” squares.
Cut a ¼” border into the edge of each of the squares, leaving some a bit of dough intact at opposite corners. Take the free corner of one side of the dough and pull it over and across the main square, to rest along the edge of the far side. Repeat with the other border, to make a diamond with a raised edge and twists in two of the corners.
Place the shaped dough in the greased wells of a mini cake pan or on a parchment-lined baking sheet. Put a tablespoon of the filling in the center and top with ¼ of a peeled fresh peach, or 3 peach slices.
Bake the Danish for 28 to 30 minutes in the cast iron pan, or 24 minutes on a baking sheet, until the dough is deep golden brown. Remove from the oven and cool for 20 minutes before devouring.