Bell pepper and cabbage should be thinly sliced. Grate the carrot. Mix the vegetables thoroughly in a big bowl.
Pack the cabbage mixture tightly into a glass jar.
Bring the water, sugar, and salt to a boil in a small saucepan. Olive oil and vinegar are added after the pan has been taken off the heat. Pour the marinade into the container with the cabbage after giving it a quick toss.
Place it in the refrigerator after it has fully cooled. Pickling should take at least 12 hours. Serve.