Preheat your oven to 425 degrees F. In a small pot, heat the blackberries with 2 teaspoons of sugar and a teaspoon of vanilla until thick and syrupy. You can also skip this step and just use heated blackberry preserves instead. Take the sliced apples and toss with the lemon juice and zest.
On a baking sheet lined with parchment paper, roll out the puff pastry square a little bit until there are no seams.
Spread the blackberry mixture over the pastry, leaving about an inch at the edges. Arrange the apples across the pastry, and brush with the warm honey (just pop it in the microwave for a few seconds). Dot the tart evenly with butter and bake for 18-20 minutes until the apples are tender and the pastry is golden brown.