An easy solution would be to do it like this
$('#ingredient option').each(
function() {
$('#list').append('<li><a href="/'+$(this).val()+'">'+$(this).text()+'</a></li>');
}
);
and the HTML
<form autocomplete="off" method="post" action="/search.html" name="asearch">
<select id="ingredient" name="attributes[3]" onchange="asearch.submit()">
<option value="16" />Biscuits
<option value="3" />Bites
<option value="6" />Bones
<option value="18" />Chews
<option value="9" />Popcorn
<option value="56" />Shanks
<option value="1" />Sticks
<option value="140" />Toy</select>
<input type="hidden" name="advanced" value="1" /></form>
<ul id="list">
</ul>
Here is the FIDDLE