You get the selected values this way:
@observable var values = toObservable(<String>[]);
void on_change(event, details, Element target) {
var el = (shadowRoot.querySelector('select') as SelectElement);
var v = <String>[];
el.options.forEach((o) => o.selected ? v.add(o.value) : null);
values.clear();
values.addAll(v);
}
Just to show the selected values on the page
<template repeat="v in values">
{{v}}
</template>