The problem with smoking the glass
Tristan Stephenson was first served a smoked cocktail by the chef Tristan Welch, who pumped applewood smoke over a rum drink from a handheld smoking gun and covered it with a small glass lid. When his first bar, Purl, opened, a smoked Rum Old Fashioned in a wax-sealed bottle with tea-scented dry-ice fog became its signature. His view today is that visible smoke and balanced flavour cannot both be had. Smoke in contact with the drink keeps changing its taste, you cannot measure smoke, and the result is at best an art and at worst impossible to repeat.
Smoke the ingredient, then dilute
His solution is to smoke an individual ingredient before mixing, saturating it to make a concentrate and then adjusting the smokiness by diluting it with the same unsmoked ingredient. That gives fine control and repeatable results. His Boulevardier à la Rue Daunou is made this way, with bourbon smoked with peated whisky and cherry-wood smoke.
What good smoke is
Smoke comes from burning wood. Below about 300 C, smouldering wood mostly breaks down cellulose and hemicellulose and makes acrid, astringent smoke. Above 300 C, lignin, about a quarter of the structure of wood, breaks down into aromatic carbonyls and phenols, which carry the sweet and spicy notes of vanilla, maple, caramel, nut, clove and cherry. At about 400 C the smoke becomes denser and carries the most flavour. If the wood catches fire, the temperature rises to about 1,000 C, which destroys the aromatics, and a smoking device keeps the wood below about 500 C by limiting airflow.
Equipment and wood
The cheapest way is a handheld smoking gun, from under £20 to over £200; the author likes the Polyscience gun at about £60. The wood goes in the crucible and is lit; a fan draws the smoke through and out of a flexible pipe, which can be directed into a mixing beaker, a cloche or a glass. Let the smoke build for five seconds before aiming it, and clean the device often, because built-up oils turn into foul-smelling compounds. High-lignin woods such as mesquite give a more intense smoke. His favourites are hickory (sweet, from barbecues), apple (lighter and fruity), oak (very bold, to be used with care) and mesquite (strong and rich).
Recipes that use these methods
The Boulevardier à la Rue Daunou is made with smoked bourbon.