Heat a large skillet or indoor grill to medium-high.

Lay out the bread slices and spread one side of each with butter. Place 4 slices (or less if there's not enough room) buttered-side down in the skillet. Top each with 2 slices of Swiss to each, a slice of tomato, 2 slices of turkey, some arugula leaves, and the remaining bread slices, buttered-side up.

Cook on both sides until bread is golden and cheese has melted. Press each sandwich down with the back of a spatula if desired to help bring the ingredients together.

Slice sandwiches into halves and serve with grapes on the side.