Definitely use a child theme to do this so your changes do not get overwritten by future theme updates.
There are rules in the theme’s style.css that prevent the header image from being wider than its container — you’ll need to add a #custom-header-image rule to your child theme’s style.css and set a larger width, probably 1200px to match the size of your new custom header. I don’t know how that might affect the rest of the layout, though, so you may need to play around with it a bit. I recommend using a browser addon like Firebug for this kind of CSS troubleshooting.
You also need to create a new functions.php file in your child theme and filter the width/height on the theme’s custom header, rather than changing the value directly in the theme. Look in the theme’s /inc/custom-header.php file to see how the custom header’s default arguments are defined. Then add a filter to your child theme’s functions.php like so:
<?php
/**
* Change default custom header size
*/
function buttercream_custom_header_args( $args ) {
$args = array(
'width' => 1200,
);
return $args;
}
add_filter( 'buttercream_custom_header_args', 'buttercream_custom_header_args', 999 );
