Not to be put off, I've tried other oil based cleansers with varying degrees of success (Vaishaly is lovely, but stings the eyes, Ren is not good, and clogged my pores more than Eve Lom, Neal's Yard rose one is not a good cleanser; I think they now market it as a treatment instead, I liked Spieza but didn't adore it.) I was browsing on a beauty e-tailer one day, as you do, and came across Saaf. The Saaf cleanser has no mineral oil, and the ingredients are:
Jojoba oil, Safflower oil, olive oil, beeswax, shea butter, natural vitamin E, grapefruit seed oil, geranium oil, lavender oil. The ingredients are 98.5% organic.
I use this with the hot cloth method - apply cleanser to dry skin, massage in to emulsify make up and grime. Take a muslin cloth, soak in warm water and ring out, then use to remove the cleanser. Rinse the face with lots of cool water. I find this cleanser removes every last scrap of make up, including tough to budge mascara, without making my eyes sting. It also leaves my skin feeling comfortable, but without a filmy layer. If I'm occasionally feeling particularly lazy or tired, I can just use this cleanser and an eye cream without having to go through the rigmarole of a whole evening routine.
The Saaf cleanser is £25 for 35g, and I bought mine from Beauty Expert. It's also available at Content Beauty.