I make my own organic potting mix using really good compost and fresh worm castings, including a few live worms for nutrient cycling. Annie Thornton's idea book features some of my work:

https://www.houzz.com/magazine/how-to-grow-vegetables-in-containers-stsetivw-vs~24753545

I use big pots, and also build organic soil amendments into the potting soil at the outset, so I don't have to add fertilizer down the road. It's like winding up a clock. You can find out more at http://www.grow-it-organically.com/fertilizing-container-vegetables.html.

In your location, you'll need to put eggplants in the hottest, sunniest, most sheltered location you can find, but these Japanese style (early) eggplants should still perform well in your climate.