Step 1

In a large skillet over medium heat, add the oil.

Step 2

Add the onions to the heated oil and cook, stirring frequently, until they are caramelized and very tender, about 20 minutes.

Step 3

Stir the brown sugar, the salt, and the pepper into the onions.

Step 4

Add the bourbon to the onion mixture and use a wooden spoon to scrape up any of the browned bits from the bottom of the skillet.

Step 5

Add 1/2 tablespoon of the butter into the onion mixture and cook, stirring constantly, until it has melted.

Step 6

Transfer the skillet from the heat and keep the onion mixture warm.

Step 7

In a medium bowl, add the cheddar cheese and the Gruyère cheese and mix until they are well-combined.

Step 8

Divide the cheese mixture into 4 equal portions, then press them into disk-like patties about the size of the bread slices.

Step 9

Divide the onion mixture into 4 equal portions, then spread 1 portion over each of the 4 bread slices.

Step 10

Top the onion mixture on each of the bread slices with 1 of the cheese patties and 1 of the remaining bread slices.

Step 11

Evenly divide 1 tablespoon of the remaining butter across the top-side of 2 of the sandwiches.

Step 12

Heat a large nonstick skillet over medium-low heat.

Step 13

Place both sandwiches, buttered-side down, in the skillet and cook until they are golden-brown on the bottom, 3-4 minutes.

Step 14

Spread 1 tablespoon of the remaining butter across the top of both sandwiches, then flip and cook until the reverse side is golden-brown and crispy, about 3-4 minutes.

Step 15

Repeat the cooking process with the remaining sandwiches and the remaining 2 tablespoons of the butter.

Step 16

Slice and serve.