Add ½ tablespoon of butter to a large cast iron skillet over medium heat. Add the onions to the skillet, cook onions till they begin to soften and carmalize. Stir occasionally, it will take about 7-10 minutes.
Remove the onions from the pan, season with some salt, and keep aside.
Slather butter on one side of the bread slices. With the skillet over medium heat, add two slices of bread buttered side down. Top each one with a generous amount of grated fontina cheese and season with a pinch of salt and pepper.Then top one side with 2 tablespoon of peach chutney and a good portion of caramelized onions and top with other piece of bread. Cook each side until deeply golden brown and the cheese has melted.
Repeat with the other two slices. Cut the grilled cheese diagonally and serve it hot.