Break the dark chocolate into pieces, and place it in a glass bowl. Then, melt it in the microwave in short bursts, or melt it over a saucepan of boiling water, whisking until smooth. Repeat this process with the white chocolate, so that you have 2 bowls of smooth, melted chocolate.
Cover 2 plates with a layer of baking paper. Dip half of the strawberries into the dark chocolate, and let them harden on one of the plates. Dip the other half of the strawberries into the white chocolate, and put them on the other plate.
Once the chocolate is beginning to harden, use either a spoon or a bottle with a narrow nozzle to drizzle the white chocolate over the dark chocolate strawberries in a side-to-side motion.
Repeat this process for the white chocolate strawberries, drizzling them with the remaining dark chocolate.
Leave the strawberries to set, about 15 minutes, and then serve. Store any leftovers in an airtight container in the fridge, and bring them back up to room temperature before serving.