What you have there seems correct. Maybe the error lies in the mut usage, maybe it's somewhere else.
The mut helper is quite vague. It is gonna be deprecated when the Ember team figures out how to do it gracefully.
You can avoid the mut helper by creating a distinct action on your controller/component.
This will let you debug: simply put a debugger statement into your action and proceed from there.
Classic Ember style:
import Component from '@ember/component';
export default Component.extend({
  timeZoneOptions: Object.freeze([
    { groupName: "Asia", options:["Kabul","Yerevan","Baku","Dhaka","Brunei","Bangkok","Shanghai","Urumqi","Taipei","Macau","Tbilisi","Dili","Kolkata","Jakarta"]},
    { groupName: "Australia", options: ["Darwin", "Eucla", "Perth", "Brisbane","Lindeman","Adelaide","Hobbart","Currie","Melbourne"]},
  ]),
  currentTimeZoneOption: null,
  actions: {
    selectTimeZoneOption(timeZoneOption) {
      this.set('currentTimeZoneOption', timeZoneOption');
    }
  }
});
{{#paper-select
  options=this.timeZoneOptions
  selected=this.currentTimeZoneOption
  onChange=(action 'selectTimeZoneOption')
  as |timeZoneOption|
}}
  {{timeZoneOption}}
{{/paper-select}}
<p>
  Current timezone option:
  {{this.currentTimeZoneOption.groupName}}
</p>
Ember Octane style:
import Component from '@glimmer/component';
import { tracked } from '@glimmer/tracking';
import { action } from '@ember/object';
export default class MyComponent extends Component {
  timeZoneOptions = Object.freeze([
    { groupName: "Asia", options:["Kabul","Yerevan","Baku","Dhaka","Brunei","Bangkok","Shanghai","Urumqi","Taipei","Macau","Tbilisi","Dili","Kolkata","Jakarta"]},
    { groupName: "Australia", options: ["Darwin", "Eucla", "Perth", "Brisbane","Lindeman","Adelaide","Hobbart","Currie","Melbourne"]},
  ]);
  @tracked
  currentTimeZoneOption = null;
  @action
  selectTimeZoneOption(timeZoneOption) {
    this.currentTimeZoneOption = timeZoneOption;
  }
}
<div class="my-component">
  <PaperSelect
    @options={{this.timeZoneOptions}}
    @selected={{this.currentTimeZoneOption}}
    @onChange={{this.selectTimeZoneOption}}
    as |timeZoneOption|
  >
    {{timeZoneOption}}
  </PaperSelect>
  <p>
    Current timezone option:
    {{this.currentTimeZoneOption.groupName}}
  </p>
</div>