Okay you know how Esme has architecture and Alice has fashion and Rosalie has cars & mechanics, Jasper? That yeehaw fucker? He's into guns. Not John Wick style with a strap of magazines and high powered rifles, Jazz enjoys the simpler things in life.
An old school pistol, a battered historic rifle. Maybe a Tommy gun if he's feeling spicy. He collects them. Every week he sets them out and cleans them meticulously, shining the golden details and waxing the wooden handles. He shoots them regularly, reloads his own ammo. The whole nine.
Whenever Edward comes around while he's cleaning them he's like "Don't get any ideas you emo bitch. These ladies are for show only."
Esme doesn't understand it but she loves that her son has another hobby so she yells a supportive "yeehaw" whenever he goes out shooting, all decked out in a shoulder holster with a rifle slung over his back. He tips his cowboy hat with one hand on the pistol at his waste and goes deep in the forest for some target "practice" (who needs to practice with perfect vampiric coordination).
Oh, and he can absolutely do the twirl-draw.