In a medium bowl, combine warm milk and 1 tablespoon sugar. Sprinkle yeast over milk and whisk to blend. Let sit until yeast is foamy, about 5 minutes.
Add eggs; whisk until smooth.
In the bowl of a stand mixer fitted with a dough hook, combine the remaining 4 tablespoons of sugar, flour, and salt. Add the milk mixture. With the mixer running on low speed, add butter, 1 piece at a time, blending well between additions.
Knead on medium speed for 1 minute. Increase speed to medium-high. Knead until the dough is smooth, about 5 minutes.
To a medium greased bowl, add the dough. Roll it to grease all sides. Cover with plastic wrap.
Let dough rise in a warm area until doubled in size, about 1 – 1 ½ hours.
When the dough is ready, punch it down and turn it out onto a lightly floured surface. Roll it into a 10×15-inch rectangle. (It should be about ¼-inch thick.)
Evenly spread lemon curd over dough making sure it covers the entire surface.
Spray a 9×13-inch baking dish with nonstick cooking spray. Set aside.
Starting on the long edge, roll the dough up tightly.
Using a very sharp knife, cut the log into 12 rolls. Place them cut side up into the prepared 9×13-inch baking pan. Let rise in a warm place until doubled, about 45 minutes to an hour.
Preheat oven to 350°F.
Bake for 25-30 minutes or until lightly golden brown. Let cool on a wire rack for at least 5 minutes.
While the rolls cool, in a small bowl, add confectioners' sugar and milk. Whisk until smooth.
Drizzle all over the warm rolls and serve.
