Combine 3 1/2 cups of flour and everything else but the butter in the stand mixer with the dough hook and mix on medium until the dough starts to come together. Feel the dough with a wet clean hand and see if it is very sticky or a bit too dry. Adjust the flour and water to get a nice smooth, slack dough that isn't overly sticky but also is not too stiff.
Add the cubed butter and continue kneading until the butter is fully incorporated and the dough is smooth. Check the window pane test to make sure it is fully developed. If not, continue kneading until it is.
Move the dough to a greased dough bucket or bowl and cover and let rise until doubled. 1 hour to 1.5 hours depending on the temp in your house.
Turn dough onto a lightly floured counter and divide into 6-8 pieces depending on how big you want the rolls and shape them (see my link in post on how to shape sandwich rolls). Place on a parchment lined baking sheet and cover with greased plastic wrap.
Allow to rise for another 30-45 minutes until a finger pressed gently into the dough doesn't bounce back and they are nearly doubled in size. Slash the tops straight down if you want to.
Bake at 375 for 15-20 minutes. The internal temp should be 200 degrees and they should be golden brown when done. Move to a rack to cool.