Step 1

Make the onions. Melt 2 tablespoons of butter with 2 tablespoons of olive oil in a large heavy skillet over medium heat. Add the sliced onions, stir to coat them in the fat, cover the pot, and cook for 5 minutes until the onions soften.

Step 2

Remove the lid and add the sugar, salt, and pepper. Stir well and put the lid back on. Reduce the heat to medium-low and cook in 5-minute intervals, lifting the lid to stir each time, until they reach a deep golden brown color, about 20 minutes.

Step 3

Add the broth to deglaze the pan, scraping up any brown spots from the bottom with a wooden spoon. Cook for about 1 minute, then stir in the thyme and remove the skillet from the heat. Transfer the caramelized onions to a heatproof bowl and carefully wipe out the skillet with a paper towel.

Step 4

Make the grilled cheese. Warm the remaining oil and butter in the skillet over medium-low heat.

Step 5

Place the 4 slices of bread in the skillet and cook until lightly toasted, about 2 minutes. Flip the bread, then evenly sprinkle the cheeses over each slice. Cover the skillet and cook until the bread is golden and the cheese has melted, about 2-3 minutes.

Step 6

Remove the skillet from the heat and carefully transfer the bread to a chopping board. Spread the caramelized onions over 2 slices of bread, then gently press the tops in place.

Step 7

Let cool for 1-2 minutes before slicing in half. Serve immediately while hot and gooey. Enjoy!