In a large bowl, whisk together the flour and salt set aside.
Heat the milk and butter together in the microwave until the butter is melted and the mixture is 110 degrees F. Stir in yeast and brown sugar. Let sit for 10 minutes.
After 10 minutes, stir the milk/butter mixture into the flour mixture.
Stir in the egg.
Once the dough has started to come together, lightly flour your surface, and knead the dough for about 2 minutes.
Place the dough in a lightly greased bowl and let rest for about 10 minutes.
While the dough is resting, make the filling: In a medium sized bowl, stir the brown sugar, lemon zest, vanilla, and shredded coconut until well combined. Set aside.
After the dough has rested for 10 minutes, lightly flour your surface again and roll it out into a rectangle (1/4 in thick).
Using your hand (or a spatula) spread the butter over the dough and then sprinkle on the lemon sugar filling.
Gently press the mixture.
Roll up the dough tightly.
Cut into 9 even pieces and place in a lightly greased 8x8 square pan.
Cover with a kitchen towel and let rise for 60 minutes.
After the rolls have risen for 60 minutes, preheat the oven to 375 degrees F.
Bake for 15 minutes.
Cover with foil and bake an additional 5 - 10 minutes, if necessary. Mine were perfect after 15 minutes.
Let cool slightly while you make the frosting.