gistfile1.js

class ApplicationRoute extends Route {
  myAction() {
    // do some fancy stuff here
  }
  
  setupController(controller, model) {
     super.setupController(controller, model);
     
     // Instead of setting on the controller, you can also inject
     // a service into this route and set the action there. 
     controller.set('someProperty', this.myAction);
  }
}

// then in application.hbs
// <MyComponent @arg1={{this.someProperty}} />

Just for link an official doc with the use of setupController:
https://guides.emberjs.com/release/routing/asynchronous-routing/

// app/routes/tardy.js

import Route from '@ember/routing/route';
import { later } from '@ember/runloop';

export default class TardyRoute extends Route {
  model() {
    return new Promise(function(resolve) {
      later(function() {
        resolve({ msg: 'Hold Your Horses' });
      }, 3000);
    });
  }

  setupController(controller, model) {
    console.log(model.msg); // "Hold Your Horses"
  }
}