Heat a large pot over low heat and add the butter. Once melted, add the onions, thyme and salt, stirring well. Cook, stirring occasionally, until the onions are golden and caramelized. This will take a full 30 to 40 minutes - or longer!
Heat a large skillet over medium heat. Spread the outsides of the bread with the thyme butter. Top one side with the grated cheese, then a spoonful of the caramelized onions. Top with the rest of the cheese and other slice of bread. Repeat with remaining bread and ingredients.
Cook the sandwich in the skillet until the cheese is melted and bubbly and the bread is golden brown. Serve immediately!
Stir the ingredients together in a bowl. This keeps great in the fridge!