Preheat the oven to 300 degrees. Slice tomatoes in half, rub with olive oil and sprinkle with kosher salt. Slow roast in the oven for 2 hours. Remove from oven and allow to cool.
Turn the temperature of the oven up to 375. Coarsely chop the onion, coat with oil and spread evenly in a roasting pan, sprinkling with salt. Set aside momentarily.
To roast the garlic: remove the outer layers of skin from the garlic bulb, leaving only the cloves in their skin attached together at the base. Carefully slice off the top of the head so that the cloves are exposed (see above picture). Place the head in a ramekin or tin foil, drizzle generously with olive oil and salt. Cover with foil.
Place both the onions and the garlic in the oven to roast for approximately 30 minutes. Check on the onions periodically and maybe give them a nudge so they cook evenly. Remove everything from the oven to cool. Once the garlic has cooled you should be able to squeeze the roasted cloves out of their skins. You should then be able to mash them like a paste. I had a smaller head of garlic that yielded around 2 1/2 teaspoons of roasted garlic paste, all of which ultimately went into the soup.
Now turn the oven way up to 475 and carefully move the oven rack to the top shelf. Give the red pepper an olive oil massage (no salt this time). Roast it for 30 minutes, turning it after 15 with tongs and then checking it every 5 minutes or so. Turn the pepper as the skin blackens. After 30 minutes remove it from the oven to cool. Once it has cooled, peel off the skin and discard the seeds.
Peel the cucumber and remove the seeds with a spoon. Dice and set aside. Chop up the basil and set aside.
Carefully ladle your tomatoes into a sturdy blender (as well as any juices on the roasting tray) and puree them. Depending on the size of your tomatoes, you should have somewhere between 7-8 cups of roasted tomato puree. You want approximately 7 cups for this recipe so set any excess puree aside. Most blenders have cup measurements right on the side to make this step easy.
Slowly add the other vegetables to the blender, pureeing everything to a smooth consistency. Also add the salt, pepper and vinegar. Drizzle in a bit more olive oil. Adjust the seasoning to your taste.
Strain the soup through a food mill, chinois or fine mesh strainer.
Serve chilled with a nice olive oil drizzled on top. And I recommend the optional garnish; it adds a nice crunch as well as more flavor!