Cook Broccolini® in a medium saucepan of boiling salted water for 2 minutes or until tender. Drain. Refresh in a bowl of iced water. Drain again. Pat dry with paper towel. Chop.
Spread butter over one side of each slice of bread. Turn over. Spread dijonnaise over four bread slices. Top with Broccolini®, ham and cheese. Season with pepper. Top with remaining slices of bread, buttered-side up.
Heat a frying pan over a medium-low heat. Cook sandwiches in two batches for 4-5 minutes on each side, or until golden and cheese is melted. Cut in half. Serve.