In a medium bowl, combine warm milk and 1 tablespoon of the granulated sugar. Sprinkle yeast over the milk and whisk to combine. Let sit until foamy, about 5 minutes.
Add the eggs to the yeast mixture and whisk until smooth.
In the bowl of a stand mixer fitted with the dough hook attachment, combine flour, remaining sugar, poppy seeds, lemon zest, and salt.
Add the milk and egg mixture to the dry ingredients.
With the mixer running on low speed, add the butter one piece at a time, letting each piece incorporate fully before adding the next.
Increase the mixer speed to medium-high and knead the dough until smooth and slightly elastic, about 5 minutes.
Transfer the dough to a greased medium bowl, turning to coat all sides. Cover the bowl with plastic wrap.
Let the dough rise in a warm area until doubled in size, about 1 to 1 ½ hours.
Turn the dough out onto a lightly floured surface and roll into a 10×15-inch rectangle, about ¼-inch thick.
Spread lemon curd evenly over the entire surface of the dough.
Starting with the long edge, roll the dough up tightly into a log.
Using a sharp knife, cut the log into 9 equal rolls.
Spray a 9×9-inch baking pan with nonstick cooking spray. Arrange the rolls cut-side up in the prepared pan.
Cover loosely with plastic wrap and let rise in a warm area until puffy and nearly doubled, about 45 minutes to 1 hour.
Preheat oven to 350°F.
Bake the rolls for 25 to 28 minutes, or until lightly golden brown on top and cooked through in the center.
Let the rolls cool in the pan on a wire rack for at least 5 minutes.
While the rolls are cooling, in a small bowl, combine confectioners' sugar and milk. Whisk until smooth and pourable.
Drizzle glaze over the warm rolls. Serve immediately or let cool completely.