Make the dough: heat the milk till lukewarm and add to a stand mixer bowl. Zest 1 lemon in the warm milk then juice. Stir together until the milk separates and thickens. Add the yeast, vanilla, 2 eggs and vigorously whisk until combined. Add the flour, salt and using the dough hook, mix until the dough turns smooth, about 5 minutes.
Gradually 70g of softened butter to the dough and continue kneading until the butter is incorporated. Cover the dough with plastic wrap and proof for 1.5 hours in a warm spot, or until doubled in size.
Make the candied lemons: Cut 5 lemons into half-moon slices and seed. In a medium saucepan, add 400g sugar, 625ml water, the lemon slices and juice any leftover lemon wedges that were too chunky to slice thin. Bring to a boil, reduce the heat to medium. Cut a circle of parchment paper and slice a hole in the center of it. Place the parchment paper directly on top of the lemons to keep them submerged. Cook for 30 to 35 minutes, until the lemons are soft, tender and translucent. Scoop out to dry (retain the liquid). Cool to room temperature. Chop to preferred size.
Make the lemon curd: Zest two lemons, and juice them plus 3 more. In a saucepan, whisk together the lemon zest, lemon juice, sugar eggs, egg yolks, and 70g of cold butter (cubed). Place the saucepan over medium heat and vigorously stir for 8 to 10 minutes. As soon as you see the first bubbles, remove off the heat. Add the remaining cubed butter (30g) and vigorously stir to in. Strain the curd through a sieve, cover and cool completely, for at least 1 hour.
Make the cream cheese frosting: In a mixing bowl, combine the cream cheese, icing sugar and juice of 1 lemon. Using a mixer or whisk, mix until smooth.
Make the sweet lemon rolls: Lightly dust the work surface with flour. Place the proofed dough on the surface and sprinkle with more flour. Roll the dough into a 12 x 15-inch (30 x 38 cm) rectangle. Place 30g softened butter on the dough and spread all over its surface, using your fingers or an offset spatula.
Dollop about 1 cup of curd all over the surface and carefully spread using an offset spatula. Reserve the rest of the curd for topping. Arrange the candied lemon in an even layer all over the dough.
Roll the 12-inch side of the dough from one end to the other. Some of the curd and lemons will ooze out as you roll—that’s totally fine. Using a long piece of floss or a knife, slice the log into 6 rolls. If any of them get loose, roll them back together. Arrange the rolls in a 10x8-inch (or larger) dish. Cover with plastic wrap and proof for 30 to 40 minutes.
Bake the rolls for 40 to 45 minutes, or until they have an internal temperature of 200°F (95°C). As soon as the rolls come out the oven, drizzle ½ cup of the lemon marmalade/candying liquid all over the buns.
Allow the rolls to cool to room temperature, about 20 to 30 minutes. Only ice those you want to eat (as the icing doesn't freeze well) -- with a dollop of cream cheese frosting and dots of lemon curd. Warm up any future buns before icing.
