admin menu: use default “general” page for theme settings using add_menu_page and add_submenu_page

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";

add_menu_page(
    "Page Title", 
    "Menu Title", 
    $desired_capability, 
    $menu_slug, 
    $menu_page_callback
);

add_submenu_page(
    $menu_slug, 
    "Submenu Page Title", 
    "Submenu Menu Title",
    $desired_capability, 
    $menu_slug, 
    $menu_page_callback
);
//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.