A martini in my opinion wants to be made with very cold ice and room temp gin.

Using frozen gin prevents the ice from contributing any water to the finished drink which is not actually a good thing.

The reason that a good martini is made with a shake-rest-shake is to give the ice a minute to mingle. too little influence from the ice and the finished drink will taste hot and boozy-harsh instead of light and insanely cold and refreshing.
And of course if you rest it too long or if your ice is not cold enough your drink will be watery.

You’ll want:
-room temp boodles gin.
-very very hard cold ice… ice that looks dry and smokes a little.
-fresh dry white vermouth, not store brand, not the pissy vinegary bottle with the mostly stuck on cap that’s been on your liquor shelf for six years.
-simple smallish green pitted unstuffed olives in brine.
– a modest old school sized martini glass, 6 ounces max. I’m partial to the Libbey #8454 4.5 oz bar glass.
-use a pro bar shaker setup, throw away the cap and nozzle thing from your stainless steel home shaker and pair it with a 16 ounce straight sided boston pint glass (you can get these with measurement lines printed on the side) and a cocktail strainer.

put your cocktail glass in the freezer.

if you have a 4.5 ounce cocktail glass put three ounces of boodles and an ounce of vermouth in your glass pint before adding ice.

if your cocktail glass is bigger scale up with the same proportion of booze and head space. pack the ice into the pint to the top.

cover with the steel shaker and wander over to the fridge, take out the olives, open them, set them down, pretend youve forgotten what you were in the middle of doing… notice the shaker, remember what you were doing, pick it up and shake it with all your might for 45 seconds or until frost forms on the outside of the shaker, which ever comes last. If the cold on your hands is excrutiatingly painful… you are doing it right.

set the shaker down.

blow on your hands and stamp your feet for a second.

Wander back over to the fridge and pretend to be looking for the olives.

remember that you already took them out and pretend to be trying to remember what you are there for.

Take the cocktail glass out of the freezer and set it by the shaker and the olives.

Pick the shaker back up and shake it again, same as the first time… 45 seconds very hard shaking.

with the shaker down and the pint up pull the two apart (might need a tap on the counter edge) and strain the liquid into the cocktail glass in one quick even pour.

if you got the proportions and the rests right this will fill the glass to the very brim.

the cocktail will look cloudy.

fish three to six olives out of the brine and sink them in the drink, don’t skewer them, just drown them, and dont be overly fastidious about shaking the brin off them first.

the drink should be almost over the edge of the glass.

have one sip if you like before the ice haze clears.

once it clears drink it purposefully, savor it but dont nurse it… you want it while it’s cold and you made it small so that you can have more than one.

when you get down to the olives try to get them with the last swallow of drink and chew them up with the cocktail… mmmm the salad course.

There are many variations on doing an honest to goodness gin and vermouth martini…

different gins, different proportions, different fruit or combinations thereof, dashes and splashes of bitters etc… but… What I’ve described here is Old School Martini 101, Simple, classic and trancendently delicious.

I’ve given this cocktail to a hundred gin haters and had a hundred instant converts. Clearly the particulars of this process are far less rigid than I’ve made them sound… but while there are probably a thousand ways to achieve results this good there are about a million ways to fuck it up and make something rancid tasting.
I suggest following closely at least once so that you know what the destination is before trying to find an alternate route to it.