Warm the milk to 95-104°F / 35-40°C and pour into the bowl of a stand mixer. Sprinkle over the yeast and sugar. If using active dry yeast, let sit 5-10 minutes until foamy. For instant yeast, move on. 240 g whole milk, 2¼ tsp instant yeast, 65 g granulated sugar
Add the flour, eggs, yolk, poppy seeds, lemon zest and salt. Fit the dough hook and mix on low until a thick dough forms, about 5 minutes. Rest for 5 minutes. 530 g all-purpose flour, 2 large eggs , 1 large egg yolk, 2 tbsp poppy seeds, 1 tbsp lemon zest,1 tsp salt
Mix on medium speed and add the softened butter a tablespoon at a time, letting each piece work in before adding the next. Keep mixing for around 10-15 minutes until smooth, glossy, and the dough pulls cleanly from the sides of the bowl. It should pass a windowpane test. 113 g unsalted butter
Shape into a ball, place in a greased bowl, cover, and let rise in a warm spot until doubled, 1.5 to 2 hours.
While the dough rises, beat together the filling ingredients until creamy and pale. Set aside at room temperature. 100 g unsalted butter, 130 g granulated sugar, 2 tbsp lemon zest, ¼ tsp salt
Line a 9x13 inch (23x33cm) pan with parchment paper.