You need to create a submenu page with the same slug as the menu page. E.g.
$menu_slug = "my_menu_slug";
$desired_capability = "manage_options"; //Or whatever you need
$menu_page_callback = "menu_page_callback_function";
"Submenu Page Title",
"Submenu Menu Title",
//Note, the 5th and 6th parameters here are the same as above. This
//overrides the first submenu title. Now clicking the
//menu title and the first submenu item will navigate to the same page,
//generated by the menu_page_callback function.