!Prepare the lemons:
Zest and juice the lemons. Divide the zest into three equal parts. One part will be used in the dough, a second part in the filling, and the final part will be sprinkled on top of the baked rolls for appearance and flavor.
Divide the juice into two equal parts, and set aside. Half of the lemon juice will be used in the lemon-sugar filling for the rolls. The other half will be used in the glaze.
!For the dough:
In the bowl of a stand mixer sprinkle the yeast over the warmed milk and let it sit for a few minutes or until foamy. With the mixer paddle, stir the softened butter, sugar, vanilla, and one cup of the flour into this milk and yeast mixture. Stir in the salt, nutmeg, and one part (1/3) of the lemon zest. Stir in the eggs and enough of the remaining flour to make a soft yet sticky dough.
Switch to the dough hook and knead for about 5 minutes, or until the dough is elastic and pliable.
Lightly grease the top of the dough with vegetable oil, and turn the dough over so it is coated in oil. Cover the bowl with plastic wrap and a towel and let the dough rise until nearly doubled — about one hour.
!For the filling:
In a small bowl, mix 1 cup sugar with the nutmeg and ginger, then work in the second part of the lemon zest (1/3) with the tips of your fingers until the sugar resembles soft sand. Slowly pour in one part (1/2) of the lemon juice, stirring. Stop when the sugar and lemon juice form a thick, clumpy mixture like wet sand. (You may use all of the reserved half of the lemon juice; you may stop before completely adding that half of the lemon juice, depending on how much juice you got from your lemons.)
!Assemble the rolls:
Lightly grease a 13x9-inch baking dish with cooking spray or butter. On a floured surface pat the dough out into a large yet still thick rectangle — about 10x15 inches. Spread the dough evenly with 3 tablespoons of very soft butter, then spread the lemon-sugar mixture over top. Roll the dough up tightly, starting from the top long end. Stretch and pull the dough taut as you roll, to keep the lemon sugar firm inside. Cut the long dough roll into 12 even rolls. Pinch the bottom of each roll closed to help keep the lemon sugar inside, and place each one, cut side up, in the prepared baking dish.
Cover the rolls with a towel and let them rise for an hour or until puffy and nearly doubled. (You can also refrigerate the rolls at this point. Cover the pan tightly with plastic wrap or a towel, and place it in the refrigerator for up to 24 hours. When you are ready to bake the rolls, remove the pan from the fridge, and let them rise for an hour before proceeding with baking.)
Preheat the oven to 350. Place the risen rolls in the oven and bake for 35 minutes or until golden brown and cooked through.
!Make the glaze:
While the rolls are baking, prepare the glaze. With a mixer, whip the cream cheese until light and fluffy. Add the remaining part lemon juice and blend until well combined. Add the powdered sugar and blend until smooth and creamy. Glaze should be thinner than frosting.
!Finish the rolls:
When the rolls are done, smear them with the cream cheese glaze, and sprinkle the final part (1/3) of the lemon zest over top to garnish. Let cool for at least 10 minutes before serving, but do serve while still warm.