It not clear to me what kind of book your looking for, or at what level. Or perhaps it would be better to say I don't believe that you have a dichotomous classification into books that only teach mathematical content versus how to do mathematics.

At a very elementary level, one book which hasn't been mentioned yet is

• How to think like a mathematician, by Kevin Houston

that I've sometimes used as a supplementary book in an intro to proofs course.

Then after one progresses to a more advanced level, I think one learns the art of mathematics not so much by explicit meta-construction, but by seeing it and figuring it out oneself. That said, there are some books which help with this more than others, and here are a few more specialized ones that I think are good:

• Course in arithmetic (or anything) by JP Serre (he's very concise and on the surface you might place this in your first category, the presentation and choice of material is excellent, and I think the process of reading Serre and figuring out the details helps one's mathematical maturity greatly)

• Problems in Algebraic Number Theory by Murty and Esmonde, or similar books in this vein (there are some basic definitions, and then a load of exercises (with hints and solutions at the end) for you to develop the theory on your own, a quasi-Moore method sort of thing)

• Foundations of Algebraic Geometry notes by Ravi Vakil (he has lots of meta-mathematical notes on why you do things a certain way, that I think help mature one's mathematical philosophy)