Why doesn't this have rum in it? That's what I think about when I think of Havana. Anyway, this is definitely an unexpected mix of ingredients for a cocktail with this name. I couldn't find any history about it online, and I don't have older cocktail books to reference where it may have come from. Curious.
A classic cobbler is just gin, sugar and some fruit as a garnish. Savoy and Café Royal have a Grape Fruit cocktail, but it is not listed as a cobbler, which has its own section at the back of the book. Lommebogen's recipe is the same as Café Royal, so I'm just going to ignore Axel calling it a cobbler.Though I suppose you could blur the line a little bit topping it with some grapefruit as well. The Savoy recipe is quite different in that it uses grapefruit marmalade instead of juice.
The Golden Fizz is essentially a Gin Fizz with an egg yolk in it. Just to be complete on the standard fizzes with egg, a Silver Fizz uses egg white instead of yolk, and a Royal Fizz uses a whole egg. The Savoy has 27 fizz recipes, all with little variations on the standard. Some swap out the main spirit, while others add another element, like an egg, liqueur, or other flavor. I can see myself exploring all of the Savoy fizzes sometime soon. Out of all of these though, I love cocktails with egg (I'm a huge flip fan) so this is definitely right up my alley.
Now that we've navigated the fuzzy world of Gin Fix and Gin Fizz, the Gin Sling gives us something with more than subtle distinctions. That said the name history for the sling is its own murky space, pulling in the Toddy and a general discussion on what defines a cocktail. I'm going to let you just go read Savoy Stomp's research on this one. You will note that the Lommebogen recipe is quite different in that it has whisky in there, along with lemon juice.
Onwards with gin drinks that have slightly confusing definitions. The Gin Fizz is a pretty straightforward cocktail, and you can see that it's similar to the previous Gin Fix, but the most common confusion for this one is with the Tom Collins. They are both like gin lemonades with soda water. At the end of the day the difference here is even more subtle that between the Fizz and the Fix.
After the Gin Cocktail, we continue the run of classic gin cocktails with the Gin Fix. You'll see that this and the Gin Fizz which follows are quite similar, but there are some subtle distinctions. The main difference I can discern between a fix and a fizz is that the fix uses regular water instead of soda water, and there is fresh fruit on it. The fruit is apparently the truly defining thing about a fix. I said subtle, right?
This is a simple cocktail in the classic definition of a cocktail. Back in the day the word "cocktail" was specifically for drinks that consisted of just liquor, a little sweetener, and some bitters. That's it. You can think of the classic old fashioned for the basic definition of a cocktail. Very simple, and they can be very nice variations on just a shot of liquor. I find it interesting that the Lommebogen recipe is pretty classic, with the sweetener, while the Savoy and Café Royal omit the sugar and up the bitters.
The Eye Opener, as the name states, is meant to get you back on your feet in the morning. Like many drinks with eggs in them, this is meant as a hangover drink. The yolk is meant to help coat your tummy, and of course the liquor is for your classic hair of the dog. The Lommebogen recipe is unlike any others I've seen. It is quite different from the Savoy and Café Royal books, as well as the modern version, most notably due to using cognac instead of rum, and adding lemon juice.
One thing to be clear about is that the East India cocktail is very different from the East Indian (note the final "n"). Both of them appear in the Savoy book, but only the East India is in Lommebogen. (For the curious, the East Indian is half each French vermouth and sherry, with orange bitters.) The big "controversy" with the East India is in the details of the sweetener.
Dubonnet is an herbal fortified wine, similar to vermouth. Vermouths traditionally have wormwood to provide the main herbal and bitter component (although not as much now), whereas Dubonnet is a brand name of a quinquina, where the major flavor is cinchona bark. Cinchona provides quinine, which gives tonic water its bitterness as well. (There is a third category of "bitter" fortified wines, called americano, which uses gentian root for bitterness. They are often considered a sub-class of quinquina, as they will often have both cinchona and gentian root.