Combine the flour and salt in the bowl of a standing electric mixer and whisk to blend. In a medium saucepan, heat the milk to 180F.  Add 4T (57g) of the butter and 1T of the sugar; stir to dissolve the sugar and melt the butter.  Let the milk mixture cool to 115F.  Stir in the yeast and let sit for 10 minutes, until foamy.  Add the remaining 3T of sugar and stir to dissolve.  Add the yeast mixture to the flour mixture and stir to combine.  Add the eggs and knead the mixture, using the dough hook, on medium speed until a dough forms into a ball and pulls away from the sides of the bowl, about 6 minutes.  While kneading, add up to 1/4 cup extra flour, 1 teaspoon at a time, if necessary for allowing the dough to pull away from the sides of the bowl.

Grease a large bowl with olive oil.  Transfer the dough to the bowl and turn to coat with the oil.  Cover the bowl with a towel and let rise in a warm place until the dough has doubled in size, about 2 hours.

Grease a nonstick muffin pan with the remaining tablespoon of butter.  Divide the dough into 12 equal pieces.  On a smooth, flat surface, cup your hand over 1 dough piece and gently roll it against the surface to form a smooth ball.  Repeat with the remaining pieces. Divide the dough balls between the muffin cups.  Cover with a towel; let rise in a warm pace for 30 minutes.  Uncover; let rise until the dough rises 2 inches above the pan, about 1.5 hours more.

Preheat the oven to 400F.  Bake the rolls until they are puffed and golden brown, 8 to 10 minutes.  Let cool slightly in the muffin pan before serving.