Function to query by custom field and category

This should work. Just make sure that meta key is Project ID.

function projects_posts() {
    global $post;

    $project_posts = get_posts( array( 

        'post__not_in' => array( $post->ID ), 
        'category_name' => 'team-resources',
        'meta_key' => 'Project ID', 
        'meta_value' => get_post_meta( $post->ID, 'Project ID', 1 ) 
    ) );

    $output="<ul>";
    foreach ( $project_posts as $project_post ) {
        $output .= '<li><a href="' . get_permalink( $project_post->ID ) . '">' . 
            apply_filters( 'the_title', $project_post->post_title, $project_post->ID ) .            
            '</a></li>';
    }
    $output .= '</ul>';

    return $output;
}