Heat a large saute pan over high heat. Add 1/2 tablespoon olive oil, garlic and mushrooms. Saute for about 3 minutes. Add remaining olive oil, onion, and continue to cook for another 3 to 4 minutes, stirring occasionally, until edges of mushrooms begin to brown.
Add chopped kale, bay leaf and thyme; stir in white wine; cover and reduce heat to medium high. Cook for about 3 minutes. Uncover, increase heat to high and cook for an additional 2 minutes.
Place mushroom mixture in a colander or sieve and press lightly to remove any excess moisture. Allow to cool to room temperature.
Preheat panini grill to 375 degrees.
Spread button on one size of each piece of bread. Spread mustard on the other side of two bread slices. Evenly distribute 1/2 West Creek Gruyere onto unbuttered side of two slices of bread. Top with kale and mushroom mixture, cover with remaining cheese, and close sandwiches with remaining slices of bread. Press down firmly on each sandwich to help ingredients stay together, then place on Panini press. Cook for about 3 minutes or until golden brown.