Start by peeling and slicing the yellow onions into thin rings. This will help them caramelize evenly and blend beautifully with the cheese.
In a skillet, melt the unsalted butter over medium heat. Add the sliced onions and a pinch of salt. Stir to coat the onions in the butter.
Once the onions start to soften (after about 5 minutes), add the water and balsamic vinegar. Continue cooking, stirring occasionally, for another 15-20 minutes until the onions are golden brown and caramelized.
While the onions are caramelizing, spread mayonnaise on one side of each slice of whole wheat bread. Flip the slices over so the mayonnaise side is down. On two of the slices, layer the reduced-fat cheddar cheese and then the caramelized onions. Top with the remaining slices of bread, mayonnaise side up.
In the same skillet used for the onions, place the sandwiches over medium heat. Grill for about 3-4 minutes on each side or until the bread is golden brown and the cheese is melted. You may want to press down gently with the spatula for even cooking.
Once golden and crispy, remove the sandwiches from the skillet. Cut them in half, serve immediately, and enjoy the melty goodness of your Grilled Cheese With Caramelized Onions!