Make the dough: Set aside 1/2 cup of flour. In a large bowl, toss the 2 and 1/4 cups flour, the sugar, salt, and yeast together until evenly dispersed. Set aside.
Heat the water, milk, and butter together in the microwave until the butter is melted and the mixture is hot to touch. About 115°F (46°C). Stir the butter mixture into the flour mixture. Add the egg and only enough of the reserved flour to make a soft dough. I only needed 1/3 cup, but you may need the full 1/2 cup. Dough will be ready when it gently pulls away from the side of the bowl and has an elastic consistency.
On a lightly floured surface, knead the dough for about 3-4 minutes. Place in a lightly greased bowl (I used non-stick spray) and let rest for about 10 minutes.
Meanwhile, make the filling: In a medium bowl, combine the sugar, lemon zest, and vanilla. Stir it around until the mixture becomes sandy. Some juices may be excreted from the lemon zest; that’s ok.
After the dough has sat for 10 minutes, roll it out into a 14×8 inch rectangle on a lightly floured surface. Spread the softened butter on top. Sprinkle the lemon sugar filling all over. Roll up the dough tightly. Cut into 11-12 even pieces and place in a lightly greased 9-inch round pan. I used a pie dish, lightly sprayed with nonstick spray. Sprinkle uncooked rolls with additional lemon zest at this point, if desired.
Loosely cover the rolls with aluminum foil and allow to rise in a warm, draft-free place for 60-90 minutes. Here is what I do: heat the oven to 200°F (93°C). Turn oven off. Place rolls inside oven and allow to rise.
After the rolls have doubled in size, preheat the oven to 375°F (190°C). Bake for 25-30 minutes until lightly browned. I covered the rolls with aluminum foil after 15 minutes to avoid heavy browning.
Make the frosting: Right before serving, top your sweet rolls with the cream cheese frosting. Using a handheld or stand mixer fitted with a paddle attachment, beat the cream cheese on medium speed until smooth. Add the confectioners’ sugar and lemon juice and beat on medium-high until creamy. Frost warm rolls and sprinkle with additional lemon zest, if desired.
Rolls are best enjoyed the same day, but stay fresh and soft in a covered container at room temperature or in the refrigerator for 5 days. Rolls (with or without frosting) freeze well, up to about 3 months. Thaw in the refrigerator and heat up however you prefer.
Make Ahead & Overnight Instructions: This dough can be made the night before through step 5. Cover with plastic wrap and let rise in the refrigerator overnight. The next morning, remove from the refrigerator and allow to rise at room temperature, about 1 hour.
Yeast: If you replace Red Star Platinum with regular active dry yeast, you rise time may be 50% longer.
Milk: I always use skim milk or 1%. Any milk fat will be fine.
Lemons: 1 medium-size lemon = approximately 1 tablespoon of lemon zest = 2 to 3 tablespoons of lemon juice.