Azure B2C - MSAL callback method doesn't call the method which return the promise?

Not sure if it's a typo in your code snippet. But as per that, it's not getting called because you are not calling :). () is missing.

ItWillCallPromise().then(function(ID){ console.log(ID)};

In MSAL.js v1, handleRedirectCallback will only be invoked when there is a hash response in the url (as a result of invoking loginRedirect or acquireTokenRedirect). Depending on the business logic of your app, you can first check if there is a hash in the url (before instantiating UserAgentApplication, which will clear the hash if one was present) and then check if a user is logged in, and then invoke ItWillCallPromise directly.

For example:

function initializeAuthAgent() {
    var authConfig =  Config();

    var hasHash = !!window.location.hash;

    authAgent = new Msal.UserAgentApplication({
        auth: {
            clientId: authConfig.clientId,
            authority: authConfig.authority,
            validateAuthority: false,
            postLogoutRedirectUri:  '/index.html'
        },
        cache: {
            cacheLocation: 'sessionStorage'
            
        }
    });

    var isLoggedIn = !!authAgent.getAccount();

    // If there is already a logged in user and were not returning from a redirect operation, immediately call ItWillCallPromise.
    if (isLoggedIn && !hasHash) {
      ItWillCallPromise()
    }

    authAgent.handleRedirectCallback(authCallback);

    


  authCallback(){
       ItWillCallPromise.then(function(ID){ console.log(ID)};
  }


  ItWillCallPromise =  function(){

 return fetch(url).then(function(a){ return a.ID;}

  }

MSAL.js v2 (aka @azure/msal-browser on npm) makes this easier, as handleRedirectPromise (which replaces handleRedirectCallback) is invoked on every page load. More details: https://github.com/AzureAD/microsoft-authentication-library-for-js/blob/dev/lib/msal-browser/docs/v1-migration.md