New face cleanser on the beauty block is BIORE Combination Skin Balancing Cleanser. It is not fragrance-free however it is oil-free.

BIORE Combination Skin Balancing Cleanser Deep Cleansing-The 'magic' is in its Skin Purifying Technology to clean & balance your face

The bottle dispenses a clear gel but when you massage into face the gel turns into a rich moisturizing lather. It feels clinging to the skin so I can feel it working in removing dirt, and it feels very refreshing. Like it wakes me up kinda feel. So, nice rich cleanser without the oil sounds like a good deal to me. Make sure you, like any facial cleansers, to not get the product into your eyes.