Normally, I’d punch you in the gut for suggesting that a Martini would be made with Vodka. But in this case, Jewel of Russia Vodka is perfect; the rye in it both masks and accentuates the whiskey.
My other gin of choice for this cocktail is Bluecoat American Gin.  The high pepper notes in Bluecoat blend seamlessly with a smokey whiskey.
You want a smokey whiskey in here, but not overpoweringly smokey like Lagavulin or Laphroiag. So, you should reach for Hibiki 12-year old.

I present to you, the Booze Guru’s Perfect Burnt Martini.

• 2.5 ounces Jewel of Russia Vodka or Bluecoat American Gin
• 1/4 ounce Hibiki 12-year old Whisky

Add ice to a Boston Shaker. Pour in the ingredients. Shake until your hands feel like they’re going to freeze off. Shake for another 10 seconds.

Strain into a cocktail glass or champagne coupe.

Garnish with a cocktail onion if desired.

Sip and contemplate the glorious universe.