I followed the thread started by Epicure US a few weeks ago and wanted to toss in my $0.02, but not until I had a chance to do some hands-on. This is where I ended up this evening.
I started with 4 good-sized shallots, one large sweet onion, and one large yellow onion. Sliced them all into thin slivers (while preheating oven to 300°). Sweated them in a large saute pan over very high heat, tossing quite often -- with about a TBSP of olive oil and a hearty pinch of kosher salt -- until they started to brown and were dryish and translucent. Took them off the heat, dosed in about a TBSP of balsamic vinegar. Buttered a square of parchment big enough to cover the pan, then pressed it over the surface of the onions. Put it in the oven. Checked at 30 min. Onions were steamy and golden brown, sizzling a bit. Stirred them, replaced the parchment. At one hour, they were dryer, darkening around the edges. Added a splash of water, stirred again. Took them out in another 20 minutes. What I ended up with was like onion marmalade. Almost clear, buttery soft, deep, dark onions, full-flavored and sweet without a hint of bitterness.
And they were delicious with the meatloaf. I daresay I'm gonna get lucky tonight.