Grease a large bowl with oil and set aside.

In a small saucepan over medium heat, warm the milk just until it starts to steam.

In the bowl of a mixer, (or in a large bowl if making by hand), combine the warmed milk, sugar, 4 tablespoons of the butter, and the salt. Mix well, then let the mixture cool slightly.

Meanwhile, mix the warm water and the yeast together in a small bowl. All the yeast to dissolve and bubble up for 5 minutes.

Add 1 1/2 cups of the flour to the milk mixture and mix until blended. Add the egg and the yeast mixture, and mix until you can no longer see the yellow of the egg yolk. 

Continue to add the flour until the dough starts to pull away from the sides of the mixer. Switch to the dough hook and knead for 2-3 minutes, or pour the dough onto a surface and knead by hand until the dough comes together.

Form the dough into a bowl and place in the greased bowl. Turn once to coat with the oil. Cover the bowl with a clean kitchen towel or with plastic wrap and set in a draft free area. Let it rise until doubled, 1 1/2 to 2 hours.

When the dough has risen, line 2 baking sheets with parchment paper or lightly grease. Set aside.

Transfer the dough to a floured surface and divide in 2 equal halves. Form each into a ball.

Working with one ball, roll the dough into a circle about 12-inches in diameter. Slightly melt the rest of the butter. (You don’t want it completely liquid, but you do want to be able to easily spread it.)  Brush half of the butter over the dough circle. 

Using a pizza cutter, sharp knife, or pastry cutter, cut the dough into 12 equal wedges. Roll the wedges up, starting at the wide end and rolling to the point. Place on the prepared baking sheet with the tip on the bottom to prevent it from unrolling.*

Repeat with the remaining dough and butter. Cover the baking sheets with clean kitchen towels and allow the rolls to rise again until doubled, about 45 minutes.

Preheat the oven to 400ºF. Remove the towels and bake the rolls until they are golden brown, 12-15 minutes. If desired, brush with a little more butter when the rolls come out of the oven.