For Puff Pastry:
1. Melt and cool 30 g butter. Sift the flour in a mound on a cool work surface and make a well in the center. Add the salt, water, and melted butter to the well. Mix with your fingers until the salt dissolves. Then use a plastic pastry scraper to pull the flour into the well and mix until blended, adding a little water if the dough is dry. Work the dough into a sticky ball with the pastry scraper. Make an X shaped incision on top of the dough, wrap in lightly floured parchment paper, and refrigerate for 30 minutes.
2. Sandwich the dry butter between 2 sheets of parchment paper and tap with a rolling pin until softened. Form the butter into a square about 3/4 inch (2 cm) thick.
3. Set the ball of dough on a lightly floured surface and flatten slightly with the palm of your hand. Then press the rolling pin into the top edge of the dough and roll out an "arm." Give the dough a quarter turn and roll out another arm. Continue to turn and roll twice more until the dough is in the shape of a cross. It should be mounded in the center, tapering out to the four arms.
4. Place the square of butter on the mounded center of dough and fold in arms, stretching the dough slightly as needed to completely seal in butter.
5. Lightly tap the top of the dough with a rolling pin to seal edges.
6. Roll out the dough to a long rectangle. The edges should be even and straight.
7. Fold the bottom third of the rectangle up toward the center, carefully aligning the edges, and brush off any flour. Fold the top third down to make a neat square and brush off any flour. You will have a neat square with the fold on the bottom.
8. Give the square a quarter turn to the left. The fold should be at the side. Roll the dough out again to a rectangle. Fold again into thirds. Gently press 2 fingertips into the dough to indicate the 2 turns have been made.
9. Wrap and refrigerate 30 minutes. Give the pastry 2 more turns and then refrigerate 30 minutes before completing the final 2 turns.
10. Divide the dough in half. On a lightly floured work surface, roll out one half about 1/8 inch (3 mm) thick; set aside. Roll out the remaining dough 1/8 inch (3 mm) thick and place on a baking sheet.
11. Using a vol-au-vent circle*, 6 inches (15 cm) in diameter, make a light imprint on one of the sheets of dough. Brush around the imprint with egg wash.
12. Make the almond cream. Cream together butter and sugars until pale and light. Add egg, beat well and stir in ground almonds and rum followed by flour. Use a piping bag fitted with a 1/2 inch (1 cm) plain tip to pipe the almond cream onto the center of the dough, leaving a ½ inch (1cm) border all around.
13. Spread the almond cream into a dome using a palette knife.
14. Place the second piece of pastry over the first and press to release any air. Seal edges.
15. Place a vol-au-vent circle, 7 inches (18 cm), lightly on cake. Use this as a guide to cut out small, uniform semi-circles, creating a scalloped effect.
16. Brush with egg wash and chill for 10 minutes.
17. Remove from refrigerator and brush with egg wash again. Using a paring knife, score the rounded top of the pastry in a pinwheel pattern.
18. Make a steam vent on the top of pastry using the tip of a knife.
19. Score the scalloped edges of the pastry in a diagonal pattern.
20. Score any remaining area of the pastry.
21. Bake at 400 degrees F (200 degrees C) until golden brown, then reduce heat to 350 degrees F (180 degrees C) for 30 minutes. Prepare syrup. Combine sugar and water, bring to the boil and reduce heat. Remove from the oven and immediately brush the top with syrup to give it a shine. Cool on a cake rack before serving.
*If you do not have a vol-au-vent circle for steps 11 and 15, use any appropriately sized circular object (plate, saucepan top, bowl, paper) to guide the cutting of the pastry.