Muddle the blackberries and basil: In a cocktail shaker, add the fresh blackberries and basil leaves. Use a muddler or the back of a spoon to gently crush the ingredients together. This releases the juices from the blackberries and the essential oils from the basil, infusing the drink with flavor.
Add the liquids: Pour in the lime juice, orgeat syrup, triple sec, and white rum into the shaker. Fill the shaker with crushed ice.
Shake it up: Secure the lid on the shaker and shake vigorously for 15-20 seconds until the mixture is well combined and chilled.
Strain: Strain the cocktail into a glass filled with more crushed ice.
Top it off: Slowly pour the dark rum on top of the drink for a gorgeous layered effect.
Garnish and serve: Garnish with a fresh blackberry and a sprig of basil for a beautiful, aromatic finish. Serve immediately and enjoy!