Make The Crushed Ice: Wrap a few handfuls of ice cubes in a clean towel or ice crusher bag and, using a mallet, rolling pin, or muddler, tap until all the ice is broken up and crushed (you want a mix of ice sizes from pea-sized to snowlike).
Shake The Cocktail: Fill an old-fashioned glass halfway with ice (not the crushed ice) and water and set aside to chill. Place honey and all but one berry in a cocktail shaker and, using a muddler, gently crush the berries to release their juices. Add the vodka, pomegranate liqueur, and juice and fill the shaker halfway with ice cubes (not the crushed ice). Close and shake until well chilled and shaker is frosted, about 10 to 20 shakes.
Serve The Bramble: Empty old-fashioned glass and fill with crushed ice. Strain cocktail over crushed ice, skewer remaining berry on a rosemary sprig, garnish drink, and serve.