Query for DatePart

I'm fairly certain that this will not work.  The "StartsWith" operator works with strings, but I'm assuming your "DOB" property is a DateTime.

How about this approach?

        public static EntityQuery GetByBirthMonthQuery(int month, int year) {
            EntityQuery empQuery = new EntityQuery(typeof(Employee));
            DateTime startDate = new DateTime(year, month, 1);
            DateTime endDate = startDate.AddMonths(1).AddTicks(-1);
            empQuery.AddClause(Employee.DateOfBirthEntityColumn, EntityQueryOp.Between, startDate, endDate);
            return empQuery;
        }

ah, yes, you did in fact say "a birthday in the current month."  I should have read more carefully.

Since EntityQueries cannot work with derived properties, these are your options:

1) create a passthrough query
2) create a view that does the Month(), Day(), Year() calculations.  Something like this:

    CREATE VIEW viwEmployeeDOB
    AS
    SELECT e.EmployeeId, Month(e.DateOfBirth) AS Month, Day(e.DateOfBirth) AS Day, Year(e.DateOfBirth) AS Year
    FROM Employee e
  
and then map this as a one-to-one related entity of the Employee entity.  then you could do a sub query against this related entity's values.

3) create a stored procedure that returns employee objects
4) create a stored procedure or dynamic entity query that returns employee ids and then create an entity query that uses the "In" operator to retrieve the employees with matching id values

These options have will side-effects if you have changed DOB in the employee object but haven't persisted yet.  Checking the database value when a local save hasn't persisted may result in unexpected behavior, so you'll need to be prepared to handle this situation.

5) if you don't have a lot of employees, or if there is some other way you can limit the number of results, you could just load all the employees into memory and use a foreach loop (or LINQ).  Of course this won't scale well unless you have another way to limit the results.