What do you think about a4? What would you do after Nd7 in that second Nakamura game?
Had a plan, but not the right plan. How do you get a good plan?

Ne6 isn't a plan - a plan takes a lot more brain power, and is normally a longer variation.
Ne6 is a tactic.

In such a position, there are two main things that stick out to me like a sore thumb. One is that White is WAY ahead in development. So, kudos to you there; you clearly understand the importance of development much better than your opponent. Secondly, Black's king is in significantly more danger. This means that with the proper strike (Ne6, like you mentioned), it's a target for you to attack. Since you asked us not to focus on this tactical opportunity, I'll leave it alone for now. Rather, I'll say that the strategy of going for the f6 square is a good one, as is committing your bishop to the a1-h8 diagonal. When your opponent's king is sitting unsafely in the center like this, it's important to get your pieces to the best possible squares (ones that will allow for tactics), try to open up the position of the king (Ne6, etc), and not trade off too many pieces (the side with less space wants to trade). Hope this helps!
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While we wait, here is a recent game of Nakamura's where I was going to ask about the bishop's plan on either b2 for white and b7 for black. Often when I do it in games, I end up like what we see in this game. The bishop gets trapped and basically I am down a bishop (and rook if I don't get it into the game). What plans can be devised here with the bishop moves (I counted 13 DSB moves in this game!!).
There is a popular war saying, that "No plan survives contact with the enemy". The first quote unquote "plan" is to simply pressure the e5 pawn. Although I just briefly glanced over the game, 10. h4 is a move I myself would definitely not play, as to me it weakens the king for no reason. If you follow the bishop moves at the start of the game, it move in accordance to black's threats, so I would argue it's not a matter of a plan, rather a matter of necessity.