private void addButtonToTable() {
TableColumn<Data, Void> colBtn = new TableColumn("Button Column");

    Callback<TableColumn<Data, Void>, TableCell<Data, Void>> cellFactory = new Callback<TableColumn<Data, Void>, TableCell<Data, Void>>() {
        @Override
        public TableCell<Data, Void> call(final TableColumn<Data, Void> param) {
            final TableCell<Data, Void> cell = new TableCell<Data, Void>() {

                private final Button btn = new Button("Action");

                {
                    btn.setOnAction((ActionEvent event) -> {
                        Data data = getTableView().getItems().get(getIndex());
                        System.out.println("selectedData: " + data);
                    });
                }

                @Override
                public void updateItem(Void item, boolean empty) {
                    super.updateItem(item, empty);
                    if (empty) {
                        setGraphic(null);
                    } else {
                        setGraphic(btn);
                    }
                }
            };
            return cell;
        }
    };

    colBtn.setCellFactory(cellFactory);

    table.getColumns().add(colBtn);

}

Problem

The setTableMenuButtonVisible of a TableView provides a mechanism to change the visibility of a table column. However that functionality leaves a lot to be desired:
The menu should remai...