How do I control a brushless DC motor without an ESC with Arduino
You cannot control a brushless motor by just plugging it in an Arduino. You might have enough parts in your junk drawer to implement a simple brushless controller, but it's not as simple as an H bridge. You need to be able to read in the Hall effect sensor inputs and switch the FETs correctly. You can google for brushless ESC schematics, but here's an example. If I were you, I'd just buy a pre-made one from HobbyKing or something.