Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Once butter is melted and shimmering, add the sliced mushrooms and cook for 5-7 minutes, stirring occasionally, until they release their liquid and start to brown.

Add the thinly sliced yellow onion to the skillet and reduce heat to medium. Cook for another 3-5 minutes, stirring until the onions are softened and translucent.

Stir in the minced garlic, dried thyme, Worcestershire sauce, salt, and black pepper. Cook for 1 minute more, until fragrant. Remove the filling from the skillet and set aside in a bowl. Wipe the skillet clean if necessary.

Spread one side of each bread slice with softened butter. For extra flavor and browning, you can also spread a thin layer of mayonnaise on the non-buttered side of two slices.

Place two bread slices, butter-side down, in the skillet (or on a griddle) over medium heat. Top each with one slice of Swiss cheese.

Evenly distribute the mushroom and onion filling over the cheese on both slices of bread. Top each with another slice of Swiss cheese.

Place the remaining two bread slices on top, butter-side up.

Cook for 3-5 minutes per side, or until the bread is golden brown and crispy, and the cheese is thoroughly melted and gooey. You may need to press down gently with a spatula to ensure even browning.

Carefully remove the sandwiches from the skillet, slice in half, and serve immediately.