Melt coconut oil, set aside in fresh bowl to cool to room temperature. Combine with olive oil once room temperature. Set aside.
Add egg, yolk, mustard, vinegar, salt/pepper, and vinegar to large mixing bowl. Mix well for 30 seconds.
SLOWLY, as in a slow drip begin to add the combined oils, while processing with whisk, hand mixer, or food processor. If you add the oil in too soon and/or fast you will not get a creamy mayonnaise.
Then, continue to blend while adding the oil in a slow stream until completely emulsified and thickened.