Add vodka, lime juice, strawberries, and basil to a pitcher and stir to combine. Then, chill in the refrigerator at least 4 hours, or overnight. Stir contents every so often, and again once it finishes marinating.
Fill copper mugs or rocks glasses with crushed iced. Add 1/3 cup vodka mixture and top with ginger beer until full. Squeeze a couple extra lime slices in each glass, and garnish with extra strawberry slices and basil leaves. Serve immediately.