At the new Tesla Diner in Hollywood, a retro-futuristic drive-in, you can catch a short film lasting about 30 minutes—the typical length of a charging session at a Supercharger—while you plug in your car. You can also get lunch (on the menu: a Tesla burger with “electric sauce”) while you use one of the 80 chargers on site.

It’s not the only attempt to reinvent the gas station in the age of electric cars. A startup called Rove opened a........

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