Heat 2 tbsp butter and 1 tbsp olive oil in a wide skillet over medium-low heat. Add sliced onions and kosher salt; cook slowly for 25-30 minutes until deep golden-brown.
Add minced garlic and fresh thyme; cook for 1 minute. Pour in beef bone broth and Worcestershire sauce to deglaze the fond, simmering for 3-4 minutes until reduced to a glossy onion jam.
Generously butter one side of each sourdough bread slice. Place 4 slices butter-side down on your workstation.
Layer each slice with shredded Gruyère, warm caramelized onions, freshly cracked black pepper, and shredded Swiss cheese. Top with remaining bread slices butter-side up.
Heat a heavy cast-iron skillet over medium heat. Place sandwiches in skillet, press gently with a spatula, and griddle for 4 to 5 minutes until crispy and golden.
Flip carefully and griddle the other side for 3 to 4 minutes until the crust is shattered-crisp and cheeses are completely melted and gooey. Serve warm immediately!