In a large, nonstick skillet, heat 1 tablespoon of the butter over medium-high heat. Add mushrooms and onion; cook, stirring frequently, 4 to 5 minutes or until mushrooms and onion are tender. Add garlic, salt, and pepper; cook 1 minute more.
To assemble sandwiches, spread one side of each baguette slice with some of the remaining butter. Top the plain sides of half of the bread slices with some of the Gruyère cheese, followed by the mushroom mixture and arugula. Top with remaining baguette slices, buttered sides up.
Heat an indoor grill pan over medium heat until hot. Place sandwiches, a few at a time, on the grill pan; weigh down sandwiches with another large pan and grill about 2 minutes or until bread is toasted. Turn sandwiches over, weigh down, and grill until remaining side is toasted.