Cut baguettes into halves. Cut cheese into thin slices and place on the lower halves of all baguettes. Add sliced sun-dried tomatoes and arugula.
Close baguettes and gently rub softened butter on all sides of the surface. Place baguettes on a medium-hot grill, close lid and leave baguettes to cook. If you press them down slightly on the grill, you will get a nice pattern.
Turn baguettes as they grill so they toast nicely on both sides.
If you are worried that the arugula will wither too much, add it to the baguettes right at the end.