Heat 1 cup of the milk in the microwave just until it is lukewarm—not hot. Stir the yeast into the milk and allow it to sit and activate for 15 minutes.
Pour this mixture into the bowl of a stand mixer, and add in 4 tablespoons of the softened butter and ⅓ cup of the granulated sugar. Mix these ingredients together on medium speed.
Mix in the eggs, one at a time, and then the salt.
Pour the 4 cups of flour into the bowl and mix it in until a wet sticky dough forms and there are no lumps of butter. Dump the dough out onto a lightly floured surface.
Knead the dough by hand for about 10 minutes on a lightly floured surface, until it is smooth and shiny. (A bench scraper is helpful to help scrape up the wet dough from the work surface.) Sprinkle a little more flour on the board as necessary if the dough is sticking.
Shape the dough into a ball and place into a large, greased bowl. Cover loosely with a piece of plastic wrap. Allow the dough to rise in a warm place for 90 minutes: it should be doubled in size.
Make the filling:
Whisk together the cup of granulated sugar, lemon zest, lemon juice, cardamom, and cinnamon. Hold this aside.
Fill, roll, and cut the dough:
Turn the dough out onto a lightly floured surface and gently press the air out. Allow the dough to rest for 10 minutes.
Line a 9x13-inch baking pan with parchment paper. (If you don't have parchment, grease the bottom and sides.)
Roll the dough out into a 12" x 18" rectangle.
Brush the dough rectangle with the melted butter. Sprinkle the sugar-spice filling over the butter distributing it evenly over the whole buttered area.
Starting at a long side, roll the dough up, jelly roll-style. Pinch along the entire, long seam until it's completely sealed.
Cut the roll into 12 equal slices: I like to use a serrated bread knife but you can also use the dental floss method if you'd prefer. Fit the slices into the prepared baking pan. Cover the pan with a clean dish towel and let the rolls rise for 30 minutes.
Bake:
Preheat the oven to 350° F.
Bake the rolls for about 30 minutes: The tops should be golden brown. Once baked remove them from the oven and allow the rolls to cool in the pan for about 10 minutes.
Make the frosting:
Beat the 4 tablespoons of softened butter until creamy. Slowly mix in the confectioner's sugar until it's completely blended with the butter. Add in the tablespoon of lemon juice and then the milk. Beat the frosting on high speed until it's creamy and fluffy.
Spread the frosting over the warm rolls, or let them cool completely before frosting. Serve the rolls warm or at room temperature.
Store leftover rolls tightly covered for up to three days. Makes 12 rolls.
Notes
Tip:
Make sure your ground cardamom is fresh, for the best flavor in these rolls.