Preheat oven to 350.
Place sun-dried tomatoes on a layer of paper towels to absorb excess oil for 5 minutes.
Cut mozzarella into 1-inch wide strips.
Transfer tomatoes to cutting board, and dice.
Place one sheet of phyllo dough on a clean cutting board; cover remaining phyllo sheets with a damp towel.
Brush single sheet with butter, then top with a second piece of phyllo dough.
Brush top sheet of phyllo, then add a third piece of phyllo.
Brush third sheet with butter.
Cut phyllo stack in half lengthwise.
Place strips of mozzarella along skinnier end of one phyllo dough stack. (Leave a 3/4" border on each end of that row.)
Top with 1/8 of the sun-dried tomatoes.
Starting at the tomato and mozzarella end, start rolling into a cigar shape.
After ingredients are enclosed, tuck in both ends, and finish rolling.
Transfer to a parchment paper lined baking sheet, seam side down.
Repeat with second stack of phyllo dough.
Repeat entire process, until all 8 cigars are made.
Bake for 25 minutes or until golden brown.