In bowl of an electric stand mixer whisk together warm water, yeast and and 1/4 tsp sugar. Let rest 5 - 10 minutes until mixture is foamy.
Fit mixer with whisk attachment. Add in 1/3 cup sugar, warm milk, 5 Tbsp butter, egg and salt to yeast mixture. Blend (butter will remain separated at this point and that's fine).
Add in 2 cups flour and mix until well combined.
Switch mixer to a dough hook attachment. Add remaining 2 1/2 cups flour and mix until dough is nearly smooth and is elastic, about 4 - 5 minutes (dough should be slightly sticky).
Transfer dough to a greased, large mixing bowl and cover bowl with greased plastic wrap. Allow dough to rise in a warm place, free from draft, until double in volume, about 1 1/2 hours.
Punch dough down all over. Divide dough into two equal portions. Shape each portion into a ball.
Roll each dough ball out on a lightly floured surface into a large circle about 13 - 14 inches across (try to keep dough as much of an even thickness as possible).
Spread each circle of dough evenly with 2 Tbsp softened butter.
Cut each circle into 4 equal quarters, then each quarter into 3 wedges (just imagine cutting pizza slices or pie slices). Roll each wedge up, beginning on wide (outside) edge.
Transfer rolls to a buttered 18 by 13-inch cookie sheet (the tip of the rolled wedge should be tucked on the bottom. Note that you can fit 3 rows of 8 rolls).
Cover rolls loosely with greased plastic wrap and let rise in a warm place until double in size, about 1 hour.
During the last 15 minutes of rising preheat oven to 375 degrees.
Remove plastic wrap and bake rolls in preheated oven for 15 - 19 minutes until golden brown.
Remove from oven and brush with remaining 3 Tbsp butter (preferably melted). Serve warm or allow to cool and store in an airtight container.