Heat a medium-sized skillet to medium high, add 1 tablespoon butter and heat to melt. Add mushrooms and cook for 3-4 minutes then add onion and cook for an additional 3-4 minutes and then add kale and red pepper flakes and sauté until onion is translucent and kale has softened. Season with kosher salt and remove from heat.
Spread butter on 1 side of each slice of bread, then stack buttered sides together. Layer 2 slices Baby Swiss on top of bread stack, then add kale and mushroom mixture then 2 more slices of Baby Swiss. Place bread buttered side down in a fry pan over medium-high heat. Cover with lid and let cook for 3-4 minutes or until golden.
Reduce heat to medium and flip sandwich to other side and cook for 2-3 minutes or until bread is toasty golden and cheese has melted. The second side will cook faster than the first so watch carefully. Repeat with next sandwich.