At first, you need to chill a martini glass by keeping it into a freezer or you can also chill it by adding water and ice into it.
After that, put ice into the cocktail mixing shaker before adding other ingredients.
Then pour in the dry vermouth and pepper vodka into a cocktail shaker for mixing it up.
Make sure that you give a proper time to mix up all of these ingredients into the cocktail mixing shaker.
Now you need to empty the glass from the ice and chilled water. It should be cold and empty.
After that pour the Cajun Martini into the chilled glass and garnish it with Jalapeno slice to give it a perfect look and taste.