In the bowl of a stand mixer with the dough hook attachment, combine 3 cups of flour with the yeast, sugar, and salt. Turn on low to mix.

Measure out milk and warm to 110F, no higher. It should feel just slightly warm to the touch.

Soften 5 tablespoons of the butter.

Add milk, butter, and egg to the mixer. Put speed on medium and beat for 2 minutes.

Add 1/2 cup flour and beat until the flour is incorporated, scraping down the sides of the bowl as needed.

Add an additional 1/2 cup and beat for 2 minutes.

Dough should form a clear ball and be only slightly sticky to the touch. If dough is still wet and sloppy, add additional 1/2 cup flour and beat for 2 more minutes.

Cover the mixer bowl with a towel and let the dough rise for at least 30 minutes. It should double in size at least.

Grease a small jelly roll pan* (see notes).

On a food scale covered in parchment paper, weigh the entire dough ball. Divide total weight by 24. This will be the weight of each roll.

Pinch off sections of dough and weigh each roll to get them as even as possible.

Roll each into a ball and pull the sides under and pinch them together to create a smooth, rounded top. Repeat and place all weighed and shapped rolls into the prepared pan.

Cover the pan with a tea towel and rise for another 30 minutes. They will rise to fill out the open space in the pan.

Preheat the oven to 375F and bake the rolls for 15 minutes, checking for browning.

Tent them with tin foil to prevent too much browning, and bake for an additional 5-10 minutes. They are done right when there is no raw dough around the center roll.

Melt remaining butter and brush onto tops of baked rolls.

Sprinkle with finishing salt and serve immediately** (see notes).