In a small saucepan, whisk the coconut milk until smooth. Sprinkle in the gelatin and whisk until incorporated. Let stand for 10 minutes so the gelatin can "bloom."

Set the saucepan over medium-high heat. Warm the coconut milk, stirring constantly, until it starts to steam and the gelatin appears to be fully dissolved. Do not bring to a boil - you just want the milk to heat to the point where the mixture is smooth. Off the heat, whisk in the syrup and vanilla.

Carefully pour the mixture into 4 ramekins or custard cups (I transferred mine first to a 4-cup measure to make pouring easier. Some people recommend straining through a sieve, but I found that my mixture was plenty smooth without this step).

Refrigerate for the panna cotta for at least 5 hours, or overnight. When ready to serve, divide the compote between the ramekins and garnish with the strawberries.