Nearly all functions in esplanade can be overwritten in a child theme. Take the esplanade_admin_header_style() function for instance. Just before that function is the following line of code if ( ! function_exists( 'esplanade_admin_header_style' ) ) :. The important part here is
if ( ! function_exists()): This means that the function it calls can be overwritten in a child theme. It is always a good practice for parent theme authors to include this function if they want to make their theme child theme friendly.
What this all means now is that you can copy the whole function esplanade_admin_header_style() { code in here } function to your child theme and edit the code as you need and that function will then be used instead of the parent theme’s function. It is important here to keep the same name for that function. So your function will look like this function esplanade_admin_header_style() { my new code in here }. Just one more thing to keep in mind, don’t copy the if ( ! function_exists( 'esplanade_admin_header_style' ) ) : part to your theme.