This noodle, or its Chinese name, is unheard of in Taiwan.
(b) The restaurant review talks about a dish in the noodle shop: "The one called 'spicy and tingly beef with wide hand-ripped noodles' brings the hypnotic pairing of chiles and Sichuan peppercorn to bits of deeply concentrated braised beef."
(A) Sichuan pepper 花椒 http://en.wikipedia.org/wiki/Sichuan_pepper
(The genus belongs in the rue or citrus family, and, despite its name, is not closely related to either black pepper or chili pepper; The husk or hull (pericarp) around the seeds may be used whole, especially in Szechuan cuisine, and the finely ground powder is one of the blended ingredients for the five-spice powder)
No wonder in US I have not seen 胡椒粉 (as called in Taiwan, and until today I have no idea it comes from 花椒).
(B) What is a peppercorn?
black pepper http://en.wikipedia.org/wiki/Black_pepper
(Piper nigrum; fruit, known as a peppercorn when dried; native to south India; Currently Vietnam is the world's largest producer and exporter of pepper, producing 34% of the world's Piper nigrum crop as of 2008)
(c) The review next says of another dish, "Then there is the biang biang dish that almost everyone gets, lamb noodles seasoned with longhorn peppers and with cumin so intensely fragrant that it seems to penetrate every taste bud you have."
The "longhorn pepper" is a kind of chili pepper. See Long Horn Peppers. Harris Seeds, undated http://www.harrisseeds.com/storefront/c-65-long-horn-peppers.aspx
("Long horn types refer to the shape of the pepper, as it resembles a bull’s horn, wide at the shoulder and grow to a pointed end")
(d) The report observes, "Biang! is essentially a cleaner, brighter, more modern sit-down version of Mr [founder David] Shi’s food stall inside the Golden Shopping Mall, an extremely ramshackle food court on Main Street in Flushing. He named the [Flushing] stall Xi’an Famous Foods."
(i) Biang! http://www.biang-nyc.com/
(ii) Xi'an Famous Foods 西安名吃 http://xianfoods.com/
I can not find the Chinese names of the owner David Shi or his son Jason Wang.
(e) The review also comments, "Cool, smooth, chewy ribbons of steamed wheat starch, liang pi are tossed with wrinkled tablets of house-made seitan and a head-clearing dose of stoplight-red chile oil."
(i) For liang pi, see liangpi http://en.wikipedia.org/wiki/Liangpi
(凉皮; a noodle-like Chinese dish made from wheat or rice flour)
(ii)
(A) For seitan, see wheat gluten (food) 面筋 http://en.wikipedia.org/wiki/Wheat_gluten_(food)
(the main protein of wheat; wheat typically contains about 14 percent protein; believed to have originated in ancient China, as a meat substitute for adherents of Buddhism; section 1.4 Macrobiotic)
(B) seitan. Wiktionary. http://en.wiktionary.org/wiki/seitan
(成蛋 or 製蛋)
(iii) Contrast 腐皮 http://zh.wikipedia.org/wiki/%E8%85%90%E7%9A%AE
(素雞，素鴨，素火腿等的主要材料便是腐皮)
(g) The review suggests, "Get the cold tofu in chile oil with pickled vegetables and get the crisp, zippily dressed lotus root salad. Get the improbably elegant canapés of rough-hewn pork sausage topped with fried quail eggs."
(i)
(A) zippy (adj; First Known Use 1904):
"full of zip: as
a: very quick or speedy <a zippy sports car>
b: strikingly fresh, lively, or appealing in style <zippy clothes>"
(B) zip (imitative of the sound of a speeding object; First Known Use 1852):
"[vi] move, act, or function with speed and vigor
[vt] to add zest, interest, or life to —often used with up" http://www.merriam-webster.com/dictionary/zip
(ii)
(A) canapé (n; French, literally, sofa; First Known Use 1863):
"an appetizer consisting of a piece of bread or toast or a cracker topped with a savory spread (as caviar or cheese)"
(B) A photo of two canapés: http://www.finncrisp.com/archives/402