Grease a 9-inch round pan and line the bottom with parchment paper. Set aside.
Place instant yeast, sugar and warm milk into the bowl of a stand mixer. Let it sit for a few minutes and then add in the 2.5 tablespoon butter, egg and salt.
Weigh the flour into a small bowl. Add ¾ of the amount of flour into the stand mixer bowl with the other ingredients and mix with the dough hook attachment, adding a bit of flour at a time until dough comes to the right consistency. You may need more or less flour depending on the temperature of your kitchen.
Knead the dough until it is a solid mass and wipes the sides of the bowl clean.
Place the dough into a large greased bowl and cover with plastic wrap. Place in a warm environment until the dough doubles in size, about 1 hour.
Punch the dough down and weigh it. Divide that number by 12 so you will know the size each roll should be to have consistent size dinner rolls.
Shape each dinner roll and place into the prepared 9-inch pan.
Cover the pan with plastic wrap and place in a warm environment until the rolls double in size, about 1 hour. Meanwhile, preheat oven to 400°F.
Bake the dinner rolls for 12 - 14 minutes or until they are golden brown.
Melt the remaining 1 tablespoon of butter and brush on to the tops of the dinner rolls right when they come out of the oven.
Let the dinner rolls cool in their pan for 10 minutes and then remove onto a wire rack.
Dinner rolls are best eaten the day they are made.