How to test custom ExceptionHandlers for annotations referenced by @ControllerAdvice?

I am working on a service broker based on the Spring Cloud Open Service Broker framework. I'm using a custom ExceptionHandler which inherits from ServiceBrokerExceptionHandler to adjust the HTTP status code for certain situations on all the ServiceBrokerRestControllers:

@ControllerAdvice(annotations = ServiceBrokerRestController.class)
public class MyServiceBrokerExceptionHandler extends ServiceBrokerExceptionHandler {

    @ExceptionHandler({MyCustomException.class})
    @ResponseStatus(HttpStatus.INTERNAL_SERVER_ERROR)
    public ErrorMessage handleException(MyCustomException ex) {
        return this.getErrorResponse(ex);
    }

}

Now I want to test it but I don't really understand how. Since the handler is applied to all controllers annotated with @ServiceBrokerRestController I don't really care about a certain controller bean let aside a certain method. I just want to "mock" some kind of ServiceBrokerRestController and given one of its methods throws a MyCustomException the web layer should return with 500 - Internal Server Error. Do I have to create a ServiceBrokerRestController dummy for that or is there a better way?

It should be an simple integration as follows. You can create a dummy controller in your test package that just throws the exceptions that you want to test.

Dummy Controller:

import org.springframework.web.bind.annotation.GetMapping;
import org.springframework.web.bind.annotation.RestController;

@RestController
public class DummyExceptionTestController {
    @GetMapping("/my-exception")
    public void customException() {
        throw new MyCustomException("My Error Message 1");
    }
}

The Integration test:

import org.springframework.beans.factory.annotation.Autowired;
import org.springframework.boot.test.autoconfigure.web.servlet.AutoConfigureMockMvc;
import org.springframework.boot.test.context.SpringBootTest;
import org.springframework.test.web.servlet.MockMvc;

import static org.springframework.test.web.servlet.request.MockMvcRequestBuilders.get;
import static org.springframework.test.web.servlet.result.MockMvcResultMatchers.content;
import static org.springframework.test.web.servlet.result.MockMvcResultMatchers.status;

@AutoConfigureMockMvc
@SpringBootTest(classes = DemoApplication.class)
public class ExceptionHandlerIT {

    @Autowired
    private MockMvc mockMvc;

    @Test
    public void testMyException() throws Exception {
        mockMvc.perform(get("/my-exception"))
                .andExpect(status().isBadRequest())
                .andExpect(content().string("My Error Message 1"));
    }


}

Exception handler and the Exception:

import org.springframework.web.bind.annotation.ControllerAdvice;
import org.springframework.web.bind.annotation.ExceptionHandler;

@ControllerAdvice
public class MyServiceBrokerExceptionHandler {

    @ExceptionHandler({MyCustomException.class})
    public ResponseEntity<String> handleException(MyCustomException ex) {
        return ResponseEntity.badRequest().body(ex.getMessage());
    }

}

public class MyCustomException extends RuntimeException {
    public MyCustomException(String msg) {
        super(msg);
    }
}