Sound like something is engaging or disengaging when I brake?

Anytime brakes make noise the issue should be looked at due to safety issues. Can you please shoot a quick video with your phone so I can hear the noise? That way I can tell for sure what's going on. You can upload it here with your response. We need to hear the noise, so we know which direction to go to help you fix the car. It takes time to upload so please be patient.

Have you looked at the brake pads in the front and rear? Also, can you tell where the noise is coming from front or rear? I have seen front pads wear out and cause noises here is how to change out the pads and rotors in case you need them.

Check out the images (below). Please upload pictures or videos in your response to the problem so we can see what's going on.