In the bowl of a stand mixer, combine flour, sugar, yeast, and salt.
In a small sauce pan, heat butter and milk until butter melts.
Cool to 120℉-130℉.
Pour over flour mixture.
Mix at low speed until ingredients are moistened, about 1 minute.
Add egg.
Mix on low until completely combined, about 1-2 minutes.
Increase speed to medium high.
Knead until dough is smooth and elastic, about 8-10 minutes.
Place dough in a covered container that has been sprayed with cooking spray, or use a proofing box set to 78℉.
Allow dough to rise until doubled in bulk, 1-2 hours.
Spray a casserole or ¼ sheet pan with cooking spray. Set aside.
Turn dough out onto a floured surface.
Roll into a 12 inch x 18 inch rectangle.
Spread dough with cranberry sauce, taking it all the way to the edges.
Starting with the long side, roll up jelly roll-style.
Slice into 1½ inch rolls.
Place rolls in prepared pan.
Cover with plastic wrap.
Allow to rise until rolls swell noticeably, about 1-1½ hours.
While rolls are proofing, heat oven to 350℉.
Bake for 20 minutes.
Cover with foil.
Bake 15 minutes.
Uncover.
Bake an additional 5 minutes, or until golden brown.