Pour vodka into large container and add fresh ingredients. Let the mixture infuse the vodka for 3 days. Vodka will be ready to drink, but gets better for the next few days after that. Pull jalapenos, cucumber, and ginger after 5 days.
To make martini, muddle 1 strawberry with 1 Tbsp simple syrup in a cocktail shaker. Add 2 oz. Infused vodka and shake mixture with ice until crackling cold. Serve in a chilled martini glass and garnish with half a fresh strawberry.
To make into a cocktail, pour 1 1/4 oz. Infused vodka over ice in a rocks glass and add gingerale.