3/4 cup sugar
1 cup fresh or frozen cranberries
1 lemon, cut into wedges
1/2 orange, sliced into thin rounds
1 1/2 cups London dry gin (such as Beefeater or Tanqueray)
1/2 cup plus 1 Tbsp. off-dry Sherry (such as Lustau East India Solera)
6 mint sprigs
Bring sugar and 3/4 cup water to a boil in a medium saucepan; stir until sugar is dissolved. Remove from heat. Pour off all but 1 cup simple syrup; refrigerate remaining syrup for another use.
Heat syrup in pan almost to a boil; reduce heat to medium. Add cranberries and simmer until they just begin to burst, 2–3 minutes. Let cool in syrup.
Place 2 Tbsp. drained cranberries and 6 Tbsp. cranberry syrup in a large pitcher. Add lemon wedges and orange slices. Using a muddler or wooden spoon, vigorously mash fruit. Stir in gin and Sherry. Let steep for 5 minutes.
Strain into a medium pitcher. Fill 3 glasses with crushed ice. Pour half of mixture into a cocktail shaker. Fill with ice; shake vigorously for 10 seconds. Strain into prepared glasses, then mound with more crushed ice. Garnish each with a mint sprig and 3 cranberries. Repeat to make 3 more cocktails.