Warm the milk, butter, sugar, and crushed cardamom pods in a small saucepan until the butter is melted and sugar dissolved, then let sit until it's lukewarm.
In the large bowl of a stand mixer, stir the flour, cardamom and salt together, then add the yeast. Strain out the cardamom pods and pour the lukewarm milk mixture into the flour mixture, and start to combine until it's almost a dough.
Then add the egg and lemon zest and stir thoroughly until the contents of the bowl come together as a soft dough.
Tip the dough onto a VERY lightly-floured work surface and knead well for five minutes (or let your mixer do most of the work), until the dough is smooth and elastic.
Place the dough into a lightly-oiled bowl and cover tightly with plastic wrap (or a damp tea towel), then leave to rise for an hour or until doubled in size.
Once the dough has finished rising, punch it down and tip it out onto a lightly-floured surface. Roll it into a rectangle about 12 inches by 8 inches. Tack down one long side to the counter with your finger.
Stir together the filling ingredients until well-combined (your butter will need to be pretty soft). Spread over the rectangle of dough, leaving 1/2 inch border on three sides and going all the way to the edge on the long side that is NOT tacked down. Sprinkle the poppyseeds across the filling.
Starting at that long side, begin carefully rolling the dough into a spiral log. With a sharp knife or cutter tool (I love my scraper), cut the log into thick slices, about 1.5-2 inches.
Place in a rimmed baking sheet or 9x13 pan, cut-side up. Leave about half an inch of space between each one, as they'll expand on their second rise and touch.
Leave to rise for about 30 minutes in a warm place. Preheat oven to 375 F regular or 355 F convection (190/170 C).
Bake for 20-25 minutes, until golden-brown. Start checking after 15 minutes and cover with foil if the buns are getting too brown.
Once done, remove from the oven and let them cool for a few minutes.
Melt the jam in a bowl in the microwave with a splash of water and stir until smooth. Brush the jam over the buns to glaze them, and allow to cool.
Then mix together the powdered sugar, lemon zest, lemon juice, an salt. If needed, add a bit more juice until the thickness is correct. Drizzle the icing over the cooled buns and allow to set before serving.