Put 1 tbsp. fresh lavender blossoms, 1/2 cup sugar, and 1/2 cup water in a microwave-safe bowl. Microwave until very warm, then stir to dissolve sugar. Let sit at least 20 minutes but no more than 1 hour, then strain syrup. Pour 1/4 cup syrup, 1/2 cup carrot juice, and 1/2 cup potato vodka such as Blue Ice into a cocktail shaker filled with ice. Shake well to blend, then strain into 2 martini glasses. Garnish glasses with lavender sprigs. Chill remaining syrup to use another time.