Mandarin Oriental Milan’s stylish new 9,600-square-foot spa aims to bring serenity to Europe’s flourishing capital of fashion, art, and design. Situated in a moodily lit subterranean level of the new 104-room hotel—just steps from the chic showrooms of top Italian brands Dolce & Gabbana, Brioni, and Salvatore Ferragamo—the six-treatment-room spa (officially opened in September) provides state-of-the-art amenities and services.

Inspired by the linear, clean lines popular in mid-century Italian estates, M…