Here’s the full solution.
First disable wpautop in your functions.php
remove_filter( 'the_content', 'wpautop' );
remove_filter( 'the_excerpt', 'wpautop' );
Then parse your content/excerpt with nl2br (a standard PHP function).
add_filter( 'the_content', 'nl2br' );
add_filter( 'the_excerpt', 'nl2br' );