Apex code showing unit tests both schedule and batch interfaces

QuickTest.cls

global class QuickTest implements Schedulable, Database.Batchable<SObject>{

    //schedule hooks
    global void execute(SchedulableContext sc){ Database.executeBatch(this); }

    //batch hooks
    global Database.QueryLocator start(Database.BatchableContext context){
        return Database.getQueryLocator([select id from account]);
    }
    global void execute(Database.BatchableContext context, List<SObject> records){ System.debug('ola'); }
    global void finish(Database.BatchableContext context){}

    static testmethod void testSchedule(){
        Test.startTest();
        final String jobId = System.schedule('QuickTest','0 0 0 3 9 ? 2022',new QuickTest());
        Test.stopTest();
        System.assertEquals('0 0 0 3 9 ? 2022',[select CronExpression from CronTrigger where id = :jobId].CronExpression);
        
    }
    
    static testmethod void testBatch(){
        Test.startTest();
        (new QuickTest()).execute(null);
        Test.stopTest();
        //verify batch job actually did something
    }

}

Doesn't look like Test.stopTest() is clever enough to wait on both scheduled apex and batch apex to complete within one unit test, hence this example. Tried multiple API versions up to 23 and no luck.