Hey Dusty, I typically just use salt, a bit of oil (whatever is required to keep things moving around when you stir), and low heat and time. You want to maximize surface area, as that is what allows for a good reduction of moisture, which facilitates expressing sugars in the produce. You can, and I do this occasionally, add a very small amount of baking soda (maybe a 1/4 teaspoon to two large onions, or four bulbs of garlic, minced, in a pan, well mixed). This changes the PH of the vegetables, and they will weep liquid more quickly, and they will caramelize much more quickly. It will taste caramelized, but it won't taste like true slowly caramelized alliums, and you have to make sure to use the bare minimum of baking soda, otherwise it will taste soapy. Using baking soda is acceptable for situations where you are adding caramelized onions, garlic, leeks, etc, to something else that is strongly flavored, but I'd never do it when making something that is mainly flavored by the caramelization itself. For instance, you'd never want to change the PH when making a very traditional French onion soup. For that application, I expect a five pounds of onions and two of shallots (which is the smallest batch of French onion I typically make, as it freezes so well) to take several hours, in a low temp oven.
I never add water, as water is the enemy of caramelization at atmospheric pressure. I've never done it, but there are pressure cooker methods to caramelize alliums more quickly. I should try that out, as I'm a big fan of pressure cookers. Having said that, the picture that is provided does not seem adequately caramelized for French onion soup, in my opinion (I think the presence of a certain required amount of water may prevent caramelization, beyond a certain point, but I'd have to test it, to be sure). For that application (I do the most traditional version, which has no beef or vegetable stock), you need the deepest flavor possible, and you want to caramelize until you hit a light mahogany color. Something just about ready to burn, but not quite there. You get that with low heat, salt, oil, surface area, and occasional stirring. I hope that helps!
Here is the French onion soup recipe I like the best, if you are interested. The only change I make is replacing a couple pounds of onions with shallot.
My favorite way of doing garlic is actually really easy. Heat your oven to 250/300. Wrap a bulb of garlic in aluminum foil. Stick the bulb in the oven for 45 minutes to an hour. Take out, once the bulb is very soft, let cool for at least an hour, and then just take the bulb apart and squeeze each clove out of the skin. Some people like to do it at higher temps for less time, but I think that brings out bitter flavors in the garlic. 45 minutes at 300 should do it just fine. You don't need to wait, if you squeeze the cloves out while wearing dishwashing gloves.
