I cannot cite peer-reviewed research, but at the very lest from my own quest for knowledge, practice (unsurprisingly) and increase in scope seem to work out pretty well.
Increase of scope being beneficial might have to do with reality being subject to a small set of basic underlying principles, so ultimately even seemingly unrelated topics of knowledge are eventually revealed to converge. So at some point you begin to see the parallels, and gain the ability to apply them to understand things better and easier. The gradual revealing of a previously obscure "big picture" if you will.
This has been the approach of some of the most prominent thinkers in human history, such as Leonardo da Vincci, Galileo Galilei and Isaac Newton just to name a few, Renaissance Men a.k.a polymaths.
Granted, polymathism limits the distance you can cover in any particular direction, but that only impedes pioneering. Spreading competence into several fields exponentially boosts the overall volume in which you can understand and apply knowledge. Seeing things from several different conceptual perspectives is far more useful than any amount of detail in seeing things from a single perspective. That is not to say that pioneering is not important, just that it doesn't really happen unless you are naturally gifted in that direction, which if you were you'd definitely know by the time you reach adolescence.
The so-called "brain training" cannot possibly result in ability you don't already have, just the improvement of what you already have. Like... you can't train math if you don't already know math, merely improving automated knowledge. What really matters in terms of enhancing learning ability is expanding your conceptual mind, and that involves the acquisition of new concepts.
Due to how the brain works, especially the chemical reward-punishment system, leaning is far from a pleasant process, the brain acts to reinforce that which it already contains, and to prevent that which it doesn't, indiscriminate as to whether the information is harmful or beneficial, so the most important thing is to be persistent, even when it doesn't seem like it yields results.
Another big impedance to learning is actually attempting to acquire knowledge as formulated by others. People's minds are fairly unique, that which works for one may not necessarily work for someone else. But also, if we don't have common terms we wouldn't be able to understand one another. So it is important to find a solution to this problem. Being 100% individualistic doesn't work, neither does being 100% conformant, because that's just memorizing, not understanding. I find it important to understand things in your own conceptual idioms, and then map the knowledge to what is already established. I suspect the opposite may work just as well for certain individuals.