"""Create error_monitor
Generated by Phi-Octopus Eden
2025-11-07 07:06:40.247028
"""

```python
from typing import Any, Callable, Dict, Optional

class ErrorMonitor:
    """
    A class for monitoring errors and providing limited error recovery mechanisms.
    
    Methods:
        __init__(self): Initializes the error monitor.
        log_error(self, message: str) -> None: Logs an error message.
        handle_exception(self, func: Callable[[Any], Any], exception_handler: Optional[Callable[[Exception], Any]]) -> Any: 
            Handles exceptions raised by a function and attempts recovery if possible.
    """
    
    def __init__(self):
        self.error_log: Dict[str, Exception] = {}
        
    def log_error(self, message: str) -> None:
        """Logs an error message."""
        import traceback
        try:
            raise Exception(message)
        except Exception as e:
            stack_trace = traceback.format_exc()
            self.error_log[message] = e
            print(f"Error logged: {e} \n{stack_trace}")
    
    def handle_exception(self, func: Callable[[Any], Any], exception_handler: Optional[Callable[[Exception], Any]]) -> Any:
        """Handles exceptions raised by a function and attempts recovery if possible."""
        try:
            return func()
        except Exception as e:
            self.log_error(f"Error in {func.__name__}: {e}")
            if exception_handler:
                print("Handling error using provided handler...")
                return exception_handler(e)
            else:
                print("No handler available for this error.")
                return None

# Example usage
def risky_function() -> int:
    """A function that might raise an exception."""
    import random
    if random.random() < 0.5:  # Randomly raises an exception
        raise ValueError("Something went wrong!")
    else:
        return 42

error_monitor = ErrorMonitor()

# Without a handler
print(error_monitor.handle_exception(risky_function, None))

# With a custom handler
def custom_handler(e: Exception) -> Any:
    """A simple custom error handler."""
    print(f"Custom handler caught {e}")
    return "Default Value"

result = error_monitor.handle_exception(risky_function, custom_handler)
print(result)
```
```python

# Example usage test cases
try:
    result1 = error_monitor.handle_exception(risky_function, None)
except Exception as e:
    print("Caught unexpected exception:", str(e))

try:
    result2 = error_monitor.handle_exception(risky_function, custom_handler)
    assert result2 == "Default Value", f"Expected 'Default Value', got {result2}"
except AssertionError as ae:
    print(f"Assertion failed: {ae}")
else:
    print("Test passed with custom handler.")
finally:
    print("All test cases completed.")

```