Heat the sugar and water in a small saucepan and heat over medium-high heat, stirring occasionally, until the sugar has dissolved, about 5 minutes. Remove from the heat and cool completely. This can be done quickly by setting the saucepan in a larger bowl partially filled with ice. The simple syrup can be made in advance and stored in the fridge for at least a few weeks.

Combine strawberries, lime juice, and soda in a high-speed blender. Add ¾ cup of the simple syrup to start. Blend until smooth. You will need to stop and scrape down sides or tamp the frozen strawberries down into the blender blades at the bottom a couple of times to make sure everything gets blended all the way.

Taste and adjust by adding more simple syrup (if you want it sweeter) or more lime juice (if you want it more tart). Pour into glasses and garnish with a slice of lime and a strawberry to serve.