Heat olive oil in a wide skillet over medium-high heat; add mushrooms in an even layer.

Cook undisturbed 4 minutes. Add onion, thyme, salt, and pepper; cook 7 to 9 minutes until dry and browned.

Cool mushrooms 3 minutes to avoid steaming bread.

Build each sandwich with 1 Swiss slice, one-quarter mushrooms, and a second Swiss slice between 2 sourdough slices.

Butter exteriors. Griddle over medium heat 3 to 4 minutes per side until bread crisps and cheese melts.

Rest 1 minute; halve.