Only show top-level links in site navigation

Had you tried depth argument (see wp_nav_menu() documentation)?

Also do I understand right that you do not setup menu manually and let theme generate it with custom callback that you have in your code?

Update

Same answer – try depth argument, only this time in wp_list_pages() call in starkers_menu() function. It should work, unless that function is never processed and not available at the time of menu running.

Do you use latest version of theme?.. If not consider updating.

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