Heat a large cast-iron skillet or frying pan over medium-low heat.
On one side of each bread slice, spread 1/2 tablespoon softened butter.
Place one bread slice buttered side down in skillet. Spread 1 to 1-1/2 tablespoons strawberry jam on bread, and top with 3/4 to 1 cup shredded Le Gruyère®. Cover with second bread slice buttered side up. Cook sandwich 3 to 4 minutes per side, or until bread is golden brown and cheese is melted. Repeat for remaining sandwiches.