Can I make Crème Brûlée using a flambé?
The final word!

After a few hours of experimenting today, this is what I discovered:


No "standard" alcohol burns hot enough to caramelize the sugar using a reasonable small amount (i.e. less than 1 tbsp).
Since there's an open flame, it will probably eventually caramelize the sugar, but the amount of alcohol required to burn that long makes the straightforward flambé method totally impractical for individual Crème Brûlées (the way that they're supposed to be served).  Testing with vanilla pudding as per Michael's suggestion using a very thin layer of sugar on top, even if you drown the entire ramekin in 80-proof alcohol, the sugar will simply dissolve before it caramelizes.
roux came up with a very good suggestion in a comment - caramelize the sugar separately and let it harden, then grind it into a powder and flambé that.  The only slight problem with this is that it grinds into the consistency of dust almost instantly, and as soon as you pour any alcohol over it, it will dissolve.


So here's how I actually (successfully) did it:


Caramelize the sugar about an hour in advance.  Pour off and let it harden.  Roux recommended using a silpat but it's perfectly possible to just dump it into a heatproof container.  If using a container, then as soon as it hardens, crack it with a knife in 2 or 3 places and let it sit for another 10-15 minutes; the cracks will spread and eventually it will "shatter" into large chunks which are easily removed.
Grind the hardened sugar using a spice grinder.  As stated above, it will take on the consistency of confectioner's sugar (beware, it is very dusty, you might want to turn the range fan on while you scoop it out of the spice grinder).  Place it in a separate (preferably wide) container.
Over time the ground sugar will actually start to crystallize again, which is why I wrote above to do this about an hour in advance.  You're aiming for a consistency that is sticky and somewhat hard but still easy to shape with your hands.
Spread a thin layer of the semi-hard sugar on each Crème Brûlée - not too thin, though, you don't want this to dissolve instantly, so aim for at least a few (2-3) mm.  It should be pretty easy to "mold" the sugar into shape.
Heat some cognac or other strong alcohol in a separate saucepan.  The amount depends on how many Crème Brûlées you're preparing, but you won't need more than a tablespoon per brûlée.  You need to get the alcohol hot if you want it to really burn when lit, but don't let it boil, otherwise it won't ignite.  This is standard flambé stuff but I'm putting it here for reference.  Personally, I let it heat up until I see a little bit of steam (but before any simmering).
Don't pour the hot alcohol into the Crème Brûlées yet.  Instead, take the saucepan off the heat and light the alcohol by itself inside the saucepan.  You should probably do this using a barbecue lighter, although I had no trouble using a butane torch.  Don't worry, it won't erupt in a massive fireball, but the saucepan will heat up very quickly so you might want to hold it with an oven mitt.
Pour a small amount of the flaming alcohol into each Crème Brûlée, and work quickly otherwise all the alcohol will burn off.  It will melt the already-caramelized sugar very quickly.
Allow all of the remaining alcohol to burn off until the flames disappear, then let it cool for at least 5 minutes.  Once the sugar begins to harden again, it will form a perfect crust!