Place the water, sugar, and pear liqueur in a medium saucepan and bring to a boil.

Meanwhile, squeeze the lemon juice into a shallow bowl. Slice off the stem and very bottom of each pear and peel the pears. Halve them from stem to bottom. With a measuring spoon or melon-baller, scoop out the core of the pear, including the vein that runs from top to bottom; then put each half into the lemon juice and rub it all over to coat the fruit.

When the liquid has boiled, reduce to low heat and add the pear halves. Simmer for 10 to 20 minutes, or until the tip of a sharp knife slides easily into the inside of one of the pear halves. The cooking time depends on how ripe the pears are. Turn off the heat when cooked and let the pears cool in the saucepan.

The pears may be made two days in advance and stored covered in the fridge with some of the poaching liquid. If making the cake right away, let the pears cool for 15 minutes and then use a slotted spoon to remove the pear halves to paper towels to dry.

To prepare the puff pastry, you will need two dinner plates or round baking pans, one that is eight inches in diameter and one that is 10 inches in diameter.

Place a piece of Gefen Parchment on the counter and sprinkle it with some flour. Unroll one sheet of puff pastry, use a rolling pin to smooth out the lines, and roll out until it is larger than the 10-inch plate. Put the plate over the pastry and run a knife around the plate to cut out a 10-inch circle. Discard the trimmings. Slide the parchment and dough circle onto a cookie sheet. Repeat with the second piece of dough and cut out another 10-inch circle of dough, and slide that dough and parchment on top of the first one. Place into the freezer for 10 minutes.

Meanwhile, prepare the almond cream. In the bowl of a stand mixer or medium bowl, beat the margarine with the whisk attachment or with an electric mixer on high speed until soft. Add the sugar, almond flour, and flour and beat until creamy. Scrape down the sides of the bowl a few times. Add the egg and pear liqueur and increase the speed to high and beat for one minute, until the mixture is light and airy.

The cream can be made three days in advance and refrigerated.

Slice the pears the long way into quarter-inch slices.

Remove the dough circles from the freezer and place one parchment and dough circle on the counter. Take an eight-inch pan or plate and press it on top of the pastry in the center to mark a smaller circle in the center of the pastry circle by pressing the plate or using a dull knife to score the circle without cutting through it.

Beat the egg yolk with one teaspoon of water and brush around the border, leaving the center empty.

Using a silicone spatula, spread the almond cream on the circle inside of the egg-brushed border (not on the border). Try to spread it as evenly as possible. Place the pear slices cut side down on top of the almond cream, fanning them out from the center, overlapping if necessary to use up most of them; you can also place some of the extra slices on top of the first layer. Sometimes I use the larger pieces and eat the really small side pieces.

Place the second pastry over the top, either by lifting the dough circle off of the parchment or placing your hand under the parchment, and gently flipping the second pastry circle over on top of the almond cream and peeling off the parchment. Stretch the dough so that you can press the edges of the two pastry sheets together to seal the top and bottom pieces. Pinch the edges to seal tightly. Make a small hole in the center of the top pastry, to let the steam out while baking.

Slide the parchment and assembled cake onto the cookie sheet and place into the freezer for 15 minutes. Preheat oven to 425 degrees Fahrenheit.

Remove from the freezer and brush the top of the cake with the remaining beaten egg yolk mixture. Use the tines of a fork to press to seal the edges tightly and create a pattern on the edge of the pastry. Use a knife to mark, but not cut through, a pattern on top of the pastry, marking curves from the center to the fork-marked border.

Bake for 15 to 18 minutes or until golden. Reduce the temperature to 350 degrees Fahrenheit and bake for another 30 minutes. Once the pastry looks sufficiently browned, drape aluminum foil on top so that it doesn’t brown further. Serve slices warm or at room temperature. Store at room temperature for up to two days.