Literally translated, 擔擔麵 means "peddler's noodles". As I noted on Wednesday, 麵 (miàn) on a menu pretty much always refers to wheat noodles. 擔 (dàn) is a less-common character in the context of the Chinese menu. The only other dish I'm aware of that includes 擔 in its name is 擔仔麵 (dàn zǎi miàn), or danzi/tan tsai noodles, a Taiwanese noodles-in-soup dish that also translates as "peddler's noodles". Wikipedia seems to think 擔擔麵 and 擔仔麵 are the same thing, but this doesn't sound right to me, and other sources also indicate otherwise.
Like mapo tofu, which I posted about a couple of weeks ago, dàn dàn miàn originates from Chengdu, the capital of Sichuan province. In my experience, though, 擔擔麵 is much less likely than 麻婆豆腐 to turn up in a dumbed-down version on Anglo-Chinese menus, perhaps because the Westernised Chinese canon already has its exemplar noodle dish in the form of chow mein.
Of the Chinese dishes I've covered so far, 擔擔麵 is perhaps the one with the greatest variation in styles. Some versions are fairly dry, others almost soupy. Some are served hot, others cold. Some recipes insist that a peanut sauce is mandatory, while others prefer a sesame-based sauce, and others still omit both peanuts and sesame. Some include Sichuan preserved vegetable (芽菜/yá cài[see footnote] or 榨菜/zhà cài), while others use chopped cucumber.
Most reputable sources, however, agree that the key to good dàn dàn miàn is the aromatic spiciness imparted by Sichuan peppercorns (花椒/huā jiāo) and carried by the oily dressing. The quality of the noodles is another important factor. At Sichuan Restaurant in West London, the noodles used in 擔擔麵 are fresh, hand-pulled noodles (拉麵/lā miàn). It's not necessary to go quite this far — just choose a type and brand of noodles that you know you like. Not too thick, not too thin, made from wheat rather than rice. Dried or fresh will do.
Like many Chinese dishes, 擔擔麵 includes a small amount of pork mince for flavour and texture. It's fine to leave this out. If you do include the pork, cook it in a wok over high heat, aiming to get nice crispy bits (but don't burn it). You can drain the cooked pork in a sieve after cooking, if there's too much residual fat for your taste.
On to the recipes... first of all, if you'd like to try making your own Sichuan chilli oil (紅油/hóng yóu/"red oil") to use in the dish, Sunflower's Food Galore has a recipe.
Sunflower also has a recipe for dàn dàn miàn, of the "sesame and peanut" school. Alternatively, take a look at Fuchsia Dunlop's recipe, which uses neither sesame nor peanut. Personally, I like to use a fair bit more Sichuan pepper than specified in either recipe. Even more variations on the theme can be found at this Chowhound thread on dan dan mian. Finally, Appetite For China has an explicitly vegetarian version that uses smoked tofu.
Footnote:  You may recall from my post on beans that 芽菜 is also the word for "beansprouts", which can cause some confusion when shopping — see Fuchsia Dunlop's post on the subject for a photo that may help you track down the actual item.