Prepare the Dough:

1. In a medium mixing bowl, whisk together milk, butter and egg until smooth.
2. In another large mixing bowl, whisk together flour, yeast, sugar and salt until evenly combined.
3. Pour the wet mixture into flour mixture. Stir well with a spatula until no dry flour is visible. Make sure to scrape off any remaining flour on the sides of the bowl.
4. Transfer the dough mixture onto a clean and dry surface. Knead the dough for 5 minutes until it turns into a soft and smooth dough ball. Because of the high fat content (butter and milk) in this recipe, the dough is much easier to knead by hand and does not require a stand mixer.

Proof the dough (first rise):

1. Transfer the dough back into the mixing bowl, lightly grease the dough ball with a little vegetable oil and cover with a lid. Covering the dough with oil will help prevent the dough from losing moisture and drying out. Let it rise at room temperature for 1 hour (or overnight in the refrigerator) until it doubles in size. 

Shape the Lemon Rolls (second rise):

1. Pour the dough onto a floured surface and use a rolling pin to roll the dough to a rectangle approximately 20x14-inches in size.
2. Gently spread softened butter evenly over the rolled dough. 
3. Whisk together sugar, 2 tablespoons lemon zest, and vanilla extract until evenly combined. Sprinkle the mixture evenly over the butter.
4. Roll up the dough tightly into a log and pinch the end edges to seal.
5. Cut into 12 even pieces using a knife or bench scraper, each about 1.5-inches in width. Arrange the rolls into a greased 9x13-inch casserole pan.
6. Cover the pan with plastic wrap or seal it in a large Ziploc bag. Let it rise (second rise) at a warmer place for 1 hour or until the rolls double in size.

Bake the Lemon Rolls:

1. Preheat the oven to 375 F.
2. Evenly sprinkle the remaining lemon zest over the rolls, and bake for 20-25 minutes until golden brown. Cover the pan halfway with aluminium foil if is browning too much. Let the rolls cool in the pan for 10 minutes.

Make the Cream Cheese Icing:

1. Using a hand mixer or stand mixer, beat the softened cream cheese on medium speed until smooth.
2. Add confectioners' sugar and lemon juice, and beat until creamy and smooth. You can also mix together using a whisk and spatula.
3. Spread the cream cheese icing over the rolls and serve hot. Sprinkle extra lemon zest on top, if desired.