Drain the canned lychees, reserving 1/4 cup of the canning syrup. In a small saucepan combine 1 cup drained lychees, chopped fresh ginger, 2 tablespoons granulated sugar and 2 tablespoons water (plus up to 1 tablespoon of reserved lychee syrup if needed).

Bring the mixture to a gentle simmer over medium-low heat, stirring occasionally until the sugar dissolves and the lychees begin to soften, about 4–5 minutes.

Remove from heat and let steep for 10 minutes to infuse the ginger flavor. After steeping, mash the lychees lightly with the back of a spoon or a fork to release more flavor.

Strain the mixture through a fine mesh sieve into a small bowl, pressing on solids to extract liquid. Discard solids or reserve a few mashed lychees for garnish. Stir in 1 teaspoon fresh lime juice to brighten the syrup. Cool the syrup to room temperature (about 10–15 minutes) or refrigerate briefly if making ahead.

Cocktail Assembly

Chill glass

Place a martini or coupe glass in the freezer for a few minutes or fill with ice water while you prepare the cocktail to ensure it is nicely chilled.

Build and shake

In a cocktail shaker add 3 oz vodka, 1 oz cooled lychee ginger syrup, 0.5 oz pineapple juice and 0.25 oz fresh lime juice. Add ice to the shaker (about 6 cubes or to fill). Secure the lid and shake vigorously for 12–15 seconds until the outside of the shaker is cold.

Double strain and serve

Discard the ice or water from the chilled glass. Double-strain the cocktail into the chilled martini/coupe using a Hawthorne strainer plus a fine mesh strainer to remove small ice shards and any pulp for a smooth appearance.

Garnish with one lychee skewered on a pick placed across the rim or dropped into the drink, and optionally a thin slice of candied or fresh ginger on the rim. Serve immediately.

If you prefer a slightly sweeter or fruitier cocktail, adjust by adding 0.25–0.5 oz extra lychee syrup or pineapple juice to taste.