In a microwave-safe bowl or small saucepan, heat the water, milk, and 4 tablespoons of butter until warm and the butter is mostly melted, about 110°F to 115°F.
⅔ cup water, ⅓ cup whole milk, 4 tablespoons unsalted butter
Pour the warm milk mixture into the dry ingredients. Add the beaten egg.
1 large egg
Using a dough hook, mix on low speed until the dough starts to come together. Add more flour a little at a time until a soft dough forms.
Increase to medium-low speed and knead for 5 to 6 minutes until the dough is smooth and elastic. Place the dough in a greased bowl, cover, and let rise until doubled in size, about 1 to 2 hours.
After the dough rises, turn the dough onto a lightly floured surface and roll it into a rectangle about ¼-inch thick.
To Make the Filling:
In a small bowl, combine the granulated sugar, lemon zest, and pinch of salt. Rub the zest into the sugar with your fingers for about 30 seconds to help release the lemon oils.
¾ cup granulated sugar, zest of 2 to 3 lemons, 1 pinch salt
Spread the softened butter evenly over the dough, going almost to the edges. Sprinkle the lemon sugar mixture evenly over the butter and gently press it down so it sticks.
6 tablespoons unsalted butter
Starting from the long side, either roll the dough into one tight log and cut it into 12 equal pieces with a sharp knife or unflavored dental floss, or use a pizza cutter to cut the dough into 12 long strips and roll each strip individually.
Arrange the rolls in the prepared baking dish. Cover and let rise in a warm, draft-free place until puffy and almost doubled in size, about 1 hour.
During the last 15 minutes of rise time, preheat the oven to 350°F.
Once the rolls have risen, gently pour the warmed heavy cream around and lightly over the rolls.
⅓ cup heavy cream
Bake for 25 to 35 minutes, or until the rolls are lightly golden brown and cooked through.
Let the rolls cool in the pan for 10 to 15 minutes before glazing.
To Make the Glaze:
To make the glaze, whisk together the powdered sugar and lemon juice. Add the lemon zest if using.