// Say if you want to test and run a method in the anonymous window by passing it a list of Ids 

Map<Id, Account> accounts = new Map<Id, Account>([SELECT Id FROM Account]);
List<Id> accountIds = new List<Id>(accounts.keySet()); // convert the Ids in the Map to a list
AccountProecssor.countContacts(accountIds);

// Actual method:

public without sharing class AccountProcessor {
    @future
    public static void countContacts(List<Id> AccountIds){
        List<Account> accounts = [SELECT Id, (SELECT Id FROM Contacts) FROM Account WHERE Id IN :AccountIds];
        
        for (Account acc : accounts){
            acc.Number_Of_Contacts__c = acc.Contacts.size();
        }
        update accounts;
    }
}

// Its test class:

@isTest
private class AccountProcessorTest {

    @isTest
    private static void countContactsTest() {
        // Load test data
        List<Account> accounts = new List<Account>();
        for (Integer i=0; i<300; i++) {
            accounts.add(new Account(Name = 'Test Account' + i));
        }
        insert accounts;
        
        List<Contact> contacts = new List<Contact>();
        List<Id> accountIds = new List<Id>();
        for (Account acc : accounts) {
            contacts.add(new Contact(FirstName = acc.Name, LastName = 'Test Contact', AccountId = acc.Id));
            accountIds.add(acc.Id);
        }
        insert contacts;
        
        // Do the test
        Test.startTest();
        AccountProcessor.CountContacts(accountIds);
        Test.stopTest();
        
        // Check result
        List<Account> accs = [SELECT Id, Number_Of_Contacts__c FROM Account];
        for (Account acc : accs) {
            System.assertEquals(1, acc.Number_Of_Contacts__c, 'Error: Expected at least one contact');
        }
    }
}

After running the method, you can go got Apex Jobs in Setup to view the future job that has run.

Note: In future methods (asynchronous) or for synchronous methods, max number of DMLs will be 2000 and max records that can be processed is 50,000. If your requirement is more, you will need to use batch apex.