Place the blackberries, honey, lemon juice, and thyme sprigs in a small saucepan over medium heat.

Cook for about 8-10 minutes, stirring occasionally and mashing the berries slightly with a fork, until the fruit breaks down and the mixture thickens into a compote.

Remove the saucepan from the heat, discard the thyme sprigs, and set the berry mixture aside to cool completely (you can place it in the fridge to speed this up).

In a large mixing bowl, whip the cold heavy cream, lemon zest, and vanilla extract until soft peaks form.

Gently fold the Greek yogurt into the whipped cream until smooth and combined.

Pour the cooled blackberry compote into the cream mixture.

Using a spatula, gently fold the fruit into the cream just 2 or 3 times to create a swirled, marbled effect; do not overmix or it will turn a solid purple.

Spoon the mixture into serving glasses or small jars.

Chill in the refrigerator for at least 30 minutes to set slightly before serving, garnished with a few fresh thyme leaves.