Melt 2 T butter in a saute pan over low heat. Add sliced onions and saute until soft, about 10 minutes, stirring occasionally.
Add beef broth and continue to cook over low heat until the pan is nearly dry, about 8 minutes, stirring occasionally. Sprinkle with 1/2 t salt.
Add bourbon whiskey and thyme leaves. Continue over low heat until the pan is nearly dry but just a little bit of liquid left, stirring occasionally.
When the onions are jammy and creamy and you want to just eat the whole pan with a spoon, remove them from the heat.
Lightly butter one side of each slice of bread and place on the counter butter side down.
Heat a saute pan over medium-low heat.
Tear 1 slice of provolone into pieces to fit each side of the bread, using one piece for each side.
Mound 1/2 oz gruyere on top of the provolone. Mound 1/2 oz gruyere on the other piece of bread.
Spoon 1/4 of the onions over one half of the bread and cheese for each sandwich.
Gently smoosh the grated cheese down on the side without onions (this makes the cheese stay in place better when you place it on the other half of the sandwich) and place over the top of the onion side.
Place the sandwich in the heated pan and cover. At about 2-3 minutes, check the color on the bottom piece of bread - it should be toasty and browned.
Flip the sandwich to toast the other side. Cover. After about 2 minutes or so, check the color.
When desired toastiness and cheese is melty, remove from heat and plate.