Plum Gin Fizz

Preheat oven to 400°F. Toss together plums and sugar on a large rimmed baking sheet until fully coated; spread in a single layer. Roast in preheated oven until fruit is soft and juicy, about 10 minutes, stirring halfway through roasting time. Let cool 5 minutes. Scrape fruit and any liquid on baking sheet into a food processor or blender; pulse until smooth, 5 to 8 pulses. Pour through a fine wire-mesh strainer into a medium bowl, pressing puree using a rubber spatula. (This may take about 10 minutes.) Discard pulp. Refrigerate, uncovered, until completely cool, about 20 minutes. (You should have about 2 cups plum puree, enough for 9 cocktails.)

Combine gin, egg white, lemon juice, and 31/2 tablespoons plum puree in a dry cocktail shaker without ice. Place lid on shaker; shake vigorously to combine, about 15 seconds. Add enough ice to shaker to fill three-fourths of the way up. Place lid on shaker, and shake until well chilled, about 10 seconds. Strain into a chilled highball glass filled with ice. Top with club soda, and garnish with lavender sprig.