In a bowl, whisk together the chickpea flour, water, olive oil, garlic, rosemary, and salt. Let the mixture rest at room temperature for at least 1 hour.
Turn on the broiler with a rack positioned 8 inches from heat. Place a 10-inch ovenproof skillet (preferably cast iron) in the oven, and get it super hot - about 10 minutes. Remove from the oven using oven mitts, add 1 tablespoon olive oil and swirl the pan around so the oil is evenly distributed. Pour in the chickpea batter and return the skillet to the broiler.
Cook for 6 to 9 minutes, or until the socca is set. The edges will be starting to brown and pull away from the sides of the pan. Remove from oven, and switch the oven to *Bake* at 425˚F.
Whisk together the vinegar and olive oil. Toss in the tomatoes, red onion, feta, and olives in the dressing until they're completely coated. Spread 1/3 of the mixture on top of the socca and return it to the oven for 15 - 20 minutes until the tomatoes are lightly blistered and the socca crisps.
Toss the spinach and oregano into the remaining salad.
Remove the pizza from the oven using oven mitts. It's easy to forget the handle is super hot, and I like to drape a towel over the handle as a reminder once I remove it from the oven.
To remove the socca from the pan, use a knife to lift an edge, and slide a metal spatula under the socca, sliding it around all edges to ensure it's not sticking to the pan (this shouldn't be a problem, but it's always good to be sure). Hold the pan over the cutting board at a 45 degree angle and gently slide the pizza onto a cutting board.
Pile the remaining salad on top and serve immediately.