Heat a griddle or large heavy skillet over medium heat.
Lay each slice of bread onto a clean work surface. Spread each slice evenly with the butter and flip over. Spread the other side of each slice of bread with 1 tablespoon red pepper jelly. Divide the mortadella between 4 slices. Top the mortadella with the Toma and fontina cheeses. Cover the sandwiches with the remaining bread slices, butter side up.
Place 2 sandwiches on the griddle. Cook until the bottoms are golden, 3 to 4 minutes. Flip and cover the skillet with a metal bowl to allow the cheese to melt, about 2 to 3 minutes longer. Repeat with the remaining 2 sandwiches. Allow the sandwiches to sit about 1 minute before slicing each in half.