Brandy

Brandy, simply put, is a distilled wine. It is categorised under Distilled Alcoholic Beverages along with Whiskey, Rum, Gin, Vodka and Tequila, but it's in a way a cross connection between Fermented liquor and distilled liquor. A Brandy typically containts 35% to 60% Alcohol by Volume ( 70-120 US proof ) and is usually consumed as an after dinner digestif.

Although Brandy is generally classified as a liquor produced by distilling wine, in a broader sense, this encompasses liquors obtained from the distillation of either pomace ( the soild remains of grapes after mashing and extraction of juice for wine making ) or fruit mash or wine.

It may be noted that Brandy like Gin is also one of the original Water of Life or eau de vie, carried over from the medieval tradition of an aquaous solution of ethanol used as a medicine.

The history of Brandy is closely tied to the development of commercial distillation in and around the 15th Century. In early 15th Century French Brandy made way for a new cross-Atlantic trade or Triangle Trade and replaced Portuguese Fortified Wine or Port from the central role it played in trade, mostly due to the higher alcohol content of the Brandy and ease of transport. However by the late 17th Century, Rum replaced Brandy as the exchange alcohol of choice in the Triangle Trade. More info on Wikipedia for the interested Brandy aficionados. Note that an Apricot Brandy can refer to the liquor (or Eau de Vie, Water of Life) distilled from fermented apricot juice or a liqueur made from apricot flesh and kernels.

Egg

Eggs are used to add viscosity and mouthfeel to cocktails, sour cocktails like Whisky Sour, tastes the best when made with added egg white. Egg whites create a creamy texture and a thick layer of foam on top of a cocktail. While unlike using just the white, adding the yolk adds a bit of a flavour to the drink, it helps emulsify the other ingredients and adds the eggnog flavour to your cocktail.
To get the silk smooth texture and mouthfeel and the foamy head without weakening the drink by melting the ice from too long shaking, which is needed to break the proteins of the egg white to froth up, dry shake the ingredients first, that is, pour all ingredients and the egg white in your shaker and shake hard without ice first, for about a minute and then add ice and shake again.

Rum

Rum is a liqour that originated in the West indies and is made by fermenting then distilling sugarcane molasses or sugarcane juice. The distillate is usually a clear liquid and is then aged in oak barrels.

Most Rums are produced in the Caribbeans and American countries, but are now produced in other sugar producing countries like PHilippines and Taiwan.

The first recorded mention of Rum comes from Barbados, in about 1650. They were originally called "kill-devil" or "rumbullion" and later on, simply Rum.

Sugar

Brown Sugar is a sucrose sugar with a distinctive brown colour from the presence of molasses, it is a partially refined or unrefined sugar containing sugar crystals and residual molasses giving it a distinctive taste and flavour of crystallised molasses or toffee. The taste of dark brown sugar is described as a caramel taste with a deep molasses flavour.
Brown sugar is used in cocktails where a caramel candy or toffee flavour is expected.

Caster Sugar is finely ground granulated sugar. It is not as fine a powdered confectioners' sugar and has a little grit to it. It is somewhere between confectioners' sugar and granulated sugar, and melts in mouth with a mild spicy feel to the tongue

Vanilla Sugar is the regular granulated sugar infused with vanilla flavour, by using vanilla pods and seeds to flavour the sugar. A home made alternative is to use vanilla sticks or pods in a jar of sugar and leave it sealed for 4 weeks to allow the vanilla flavour to infuse. Or to use granulated sugar and vanilla extract and blend in a mixer, although this ends up in powdered sugar.

Milk Hot

Milk can do wonders to your regular cocktail. For a rich creamy cocktail, milk does wonder .You may argue that milk as it is made of fat, and being low in acid, will easily curdle if its mixed with alcohol.
Best way to get a rich and creamy cocktail is to use bourbon, milk will soften its whiskey flavour. If you are looking for some spicier yet creamy cocktail go for Scotch with milk cocktails, they'll surely set you holiday mood.