2/3 cup milk, heated to 110 degrees F
5 tbsp sugar, divided
2 tsp dry active yeast
2 3/4 cups (344g) AP flour, may need additional
3 tbsp poppy seeds
1 tsp salt
1/2 cup (113g) butter, softened, cut into pieces
1 tbsp butter, melted
Place heated milk in a 2-cup measuring cup, stir in 1 tbsp of sugar. Sprinkle yeast over and whisk to blend. Let sit for 5 minutes until foamy. Add eggs and whisk until smooth. Combine flour, poppy seeds, salt and remaining sugar in the bowl of a stand mixer fitted with a dough hook. Add milk mixture. With mixer running, add butter, one piece at a time, blending well between additions. Mix on medium speed 1 minute. Knead on med/high speed until dough is soft and silky, about 5 minutes. If it seems too wet, sprinkle in 1 tbsp of flour at a time until it becomes a ball.
Grease a medium bowl with butter and place dough in bowl. Brush remaining butter on top of dough and cover with plastic wrap. Let rise in a warm area until doubled. 1-2 hours.
1 cup (226g) butter, softened
1 cup (200g) sugar
1 cup (140g) almonds, roughly chopped
1/2 tsp salt
Combine the butter and sugar, in the bowl of a stand mixer, with the whisk attachment. Beat until light and fluffy, 2-3 minutes. Set aside.
On a lightly floured surface, roll out dough to 12x16" rectangle, about 1/4" thick. Have 1 long side facing you. Spread filling over the dough, leaving a 1" border on the side farthest from you. Sprinkle almonds evenly over and gently press into the surface. Beginning with the side closet to you, tightly roll into a log. Pinch together the ends and tuck under. Using a large serrated knife, cut into 9 equal sized pieces. Place buns cut side up, 3 rows of 3, in a 9" square pan. Cover with a kitchen towel and let rise until doubled, 45-60 minutes.
1 cup (125g) powdered sugar
2 tbsp milk
1 tsp vanilla
pinch of salt
Whisk all the ingredients together until combined, adding more milk if too thick . Set aside
Oven 350 degrees F.
Whisk the egg with 1/2 tsp water. Brush over the tops of the risen buns. Bake until buns are golden brown and filling is bubbling, about 50 minutes. Right after removing the buns from the oven, spread the frosting over evenly. Let cool slightly, eat warm.
Bun recipe modified from @BonAppetit