Wash, hull and roughly chop the strawberries. Muddle the chopped strawberries with the lime juice in a glass or cocktail shaker. Alternatively, if you prefer the mixture smoother (and especially if making a larger batch), blend the strawberries and lime juice to a puree.
Add plenty of ice in a copper mug or glass. Add the strawberry-lime mixture then add the vodka. Top up with ginger beer and stir gently to mix.
Decorate with slices of lime and strawberry (you could also add a sprig of mint).
Notes
In particular for larger batches, I suggest blending the strawberries to make a smoother puree as muddling can leave chunks that are a little less easy to drink and don't mix as well. It's tricky to blend for just one drink, but for multiple, it feels more worth the extra things to wash. If your strawberries are not that sweet then you may want to add up to ½ oz (1tbsp, 15ml) simple syrup to help sweeten them, or else sprinkle a little sugar over the chopped berries and leaving to macerate a few minutes before muddling/blending. Though bear in mind this is not really a sweet cocktail.