Add butter and olive oil to a large skillet, melt over medium-low heat.
Add onion slices and salt and cook stirring occasionally until jammy and golden brown, about 35-40 minutes.
Add cooking wine and fresh thyme, use a wooden spoon to deglaze pan and continue heating for 3-4 minutes.
Set aside and clean pan for next step.
Arrange bread slices on a flat surface, and spread mayonnaise on both sides of each slice of bread then flip over.
Divide caramelized onions evenly over 4 slices of bread.
Divide gruyere evenly over onions,.
Top gruyere with slice of provolone, then top with bread.
Heat skillet over medium heat. Cook sandwiches 3 minutes on each side, flipping carefully. You may need to cook in batches.
Cut in half and serve warm.