Place the blood orange quarters and mint leaves into a cocktail shaker. Gently crush with a muddler or the end of a wooden spoon until the blood orange quarters have released their juice. Add the bourbon and fill the shaker with ice. Put the lid on the shaker and shake vigorously for 10 seconds then strain into a cocktail glass. Add ginger beer and fill glass with crushed ice. Garnish with sprigs of mint.