In a small saucepan, combine the blackberries, lime juice, and 1 teaspoon honey over medium heat. Cover and cook until bubbling. Remove lid and whisk until the mixture thickens. Pour into a small container, cover, and refrigerate.
Clean the saucepan and add raspberries, lemon juice, and 1 teaspoon honey. Cook, covered, over medium heat until bubbling. Remove lid and whisk until thickened. Pour into small container, cover, and refrigerate.
Clean the saucepan again and add strawberries and remaining 1 teaspoon honey. Cook, covered, over medium heat until bubbling. Remove lid and whisk until thickened. Pour into small container, cover and refrigerate until cold, 1-2 hours.
In a small bowl, beat the cream until stiff peaks form. Beat in the sufar and seeds from vanilla bean.
In 2 large bowls or 4 parfait glasses, add a layer of blackberries. Top with a layer of cream. Add a layer of raspberries, then another layer of cream. Top with strawberries and garnish with more cream or fresh berries.
Serve immediately or refrigerate until ready to serve.