Fill a cocktail shaker with ice. Add the vodka, blood orange juice, vermouth and simple syrup. Fit the lid tightly on the shaker and shake vigorously for 30 seconds until the outside of the shaker is icy cold.
Strain the cocktail into a martini or coupe glass and garnish with a thin slice of blood orange.
Notes
I like to squeeze blood orange juice in advance and keep it chilled, so there's no fuss when assembling the cocktail.