I'm sure the body makes its own HDL cholesterol; you are not supposed to eat it but foods that can be used to synthesise it.
There are plenty of ways to increase your HDL, but ingesting more cholesterol isn't one of them. That's just silly. Eat more monounsaturated fats and fiber, and keep your omega-3 ratios favorable. Do aerobic exercise. Stop drinking and smoking. Avoid trans fats.
Really? I did not know that ingested cholesterol could not be modified to become hdl or ldl. I figured the body may have some way to convert it, given the molecular similarity. They are very very close, and so that is surprising, but not unbelievable by any means!
Oh, the body can modify (and use) ingested cholesterol, sure, but the effect is small compared to that of trans and saturated fats. Some studies show no effect whatsoever from ingested cholesterol, and I'm not aware of any showing an increase in HDL without a corresponding increase in LDL. Regardless, most of your HDL is going to be produced by your liver anyway based on the factors I listed earlier.