Make syrup: Bring sugar and water to a boil, then let cool to room temperature. Steep mint in syrup for 12 to 24 hours in fridge, then strain.
Make cocktail: In a copper mug, stir Seedlip, mint syrup, and lime juice together. Top with crushed or shaved ice and pour ginger beer over to fill. Garnish with a lime wheel and mint sprig if you like.
*Seedlip is the world’s first nonalcoholic spirit. Produced in London, it tastes similar to gin and is available stateside at select Whole Foods Markets and boutique liquor shops.