Cream the Butter and sugar, scraping down sides as necessary.
Add egg to running mixer. Scrape down sides as needed. Beat until smooth. Add vanilla.
Sift the flour and salt together. Add to creamed butter a portion at a time.
Mix until a smooth ball forms.
Flatten dough to about 1 inch thick. Wrap in parchment paper and chill for about 1 hour. Chilling makes the dough easier to work with.
Roll out dough, between 2 pieces of parchment to about 1/4 inch thick.
Cut into 3 inch circles. Fill with about 2 tsp. of filling. Crimp 3 corners to make traditional hamantaschen shape (like a triangle). Place on parchment lined cookie sheet spacing about 2 inches apart to allow for spread.
Chill shaped, filled cookie in refrigerator for about an hour or until well chilled. This is to limit the "melt" of the cookie part when put into the oven.
Preheat oven to 375. Temperature is a little higher to set the crust before the cookie melts and loses shape.
Verify that your corner crimps are good and bake until golden. Times will vary with ovens and temperature. Check after 10 minutes.
Bake until golden on bottom and corners. Times will vary based on how cold the dough is and oven temperature. Start checking after 10 minutes.
Remove zest from the lemons and juice them. Reserve 9 grams of the zest and 90 grams of the lemon juice.
Whisk the juice, zest, eggs, salt and first sugar (100g) until smooth.
Quarter the lemon shells and then thinly slice.
Place the lemon strips into a pan, cover with water, bring to a boil and cook for 3 minutes.
Drain and pat dry.
Place strips and remaining sugar (50g) in a pan and cook over medium high heat, stirring constantly, until caramelized. Let cool for 2 minutes.
Combine caramelized strips and lemon juice mixture in a pan. Cook on low heat until thickened. Remove from heat and stir in butter. Allow to cool before use.
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.