Preheat a heavy skillet or griddle over low heat until a spatter of water disappears quickly.
Spread bottom half of muffin with cranberry sauce; top with sliced turkey and cheddar cheese. Spread butter on outside top and bottom of muffins.
Place bottom-side down in preheated skillet. Place a heavy saucepan weighted with 2 canned goods on top to flatten panini. Cook 3 minutes. Turn and cook on second side 3 minutes with weight in place until cheese starts to melt into pan.