For me there's a small difference.
"I want to learn cooking" emphasizes more all aspects of cooking. Not just the required specifics of a particular meal, dish, or particular recipe, but more depth. That is I want to learn more than *just* how to cook something. I may want to know the several ways of cooking it, the history, the variations, etc. And I want to know about cooking in general - I want to understand it almost as much as I was trying to understand any particular area of knowledge.
"I want to learn how to cook" *can* mean the above, but for me it generally means I have less requirements in what I want to know. I just want to know the practicalities of cooking - ie how to prepare basic meals. I'm not so interested in treating 'cooking' as something I need to go into any great depth with.
This is my take on the 2 sentences :)