Process the poppyseeds and first sugar till poppyseeds are ground and mixture starts to clump, feeling damp. This may take some time.
Bring milk and butter to a simmer.
Whisk together the remaining sugar and the eggs
Temper egg/sugar mixture with some of the simmered milk/butter mixture. Mix into remaining milk/butter mixture. Return to heat and cook slowly until thickened.
Strain into a clean bowl and mix in poppyseed mixture. Cover tightly and chill well.