In a saucepan, combine the heavy cream, whole milk, sugar, chamomile tea leaves, and salt. Heat over medium heat until the mixture is warm and the sugar is dissolved, but do not boil.

Remove from heat and stir in the vanilla extract. Let the mixture cool to room temperature, then refrigerate for at least 2 hours or until chilled.

In a blender, combine the blackberries, sugar, and lemon juice. Blend until smooth. Strain through a fine mesh sieve to remove seeds, if desired.

Pour the chilled ice cream base into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.

Transfer half of the ice cream to a container, then drizzle half of the blackberry swirl over it. Repeat with the remaining ice cream and blackberry swirl.

Use a knife or skewer to gently swirl the blackberry mixture into the ice cream. Cover and freeze until firm, about 2-4 hours.