Whisk the flour, baking powder, salt and 50 g sugar in a 28 cm / 11-inch mixing bowl. Rub in the cold butter with your fingertips until the mixture looks like coarse crumbs with a few pea-size bits left.

Stir in the sour cream and egg yolks with a fork, then knead on the counter for about 1 minute until the dough is smooth and just holds together. Divide into 8 pieces of about 100 g each, flatten into rectangles, wrap and chill for 30 minutes.

While the dough chills, bring the milk, 50 g sugar, honey and 40 g butter to a gentle simmer in a 2-quart / 1.9 L saucepan, stirring until the butter melts. Stir in the poppy seeds and cook over medium-low heat for 8 to 10 minutes, stirring often, until the mixture is a thick paste that leaves a trail when you drag the spoon through it.

Take the pan off the heat and stir in the lemon zest and vanilla. Let the filling cool to lukewarm, about 20 minutes.

Heat the oven to 190 C / 375 F with racks in the upper and lower thirds. Cut parchment to fit two 33 x 46 cm / 13 x 18 inch baking sheets.

Roll one dough piece on a lightly floured parchment sheet to a 20 x 30 cm / 8 x 12 inch rectangle, about 1.5 mm thick. Prick it all over with a fork. Roll a second piece beside it on the same parchment with a small gap, then slide the parchment onto a baking sheet. Repeat for the second tray, keeping the remaining 4 pieces in the fridge.

Bake both trays for 10 minutes, swapping their positions halfway, until the sheets are pale gold with slightly darker edges. Roll the remaining 4 pieces on fresh parchment while the first batch bakes, then bake them the same way once the first sheets are lifted off the trays.

Slide the baked sheets onto a rack and cool for 5 minutes. Trim ragged edges with a sharp knife so the sheets stack evenly.

Set one sheet on a board or flat serving platter and spread about 80 g (4 tbsp) of poppy filling over it, right to the edges. Repeat with 6 more sheets, pressing each one down gently. Finish with the eighth sheet.

Stir the sour cream and powdered sugar together and spread it over the top sheet. Cover loosely and refrigerate for at least 6 hours.

Cut with a serrated knife in a gentle sawing motion into 12 slices, each about 5 x 10 cm, wiping the blade between cuts. Serve chilled or after 20 minutes at room temperature.