Preheat oven to 425°F. Remove puff pastry from fridge and trim to fit baking sheet or pizza stone.
Using a fork, prick around the edges of the puff pastry to create an indentation around the perimeter. Brush edges gently with egg whites.
Quickly layer cheese, prosciutto, sun-dried tomatoes, and basil in the center of the pastry. Drizzle with olive oil and sprinkle flaky salt.
Transfer to oven and bake until golden brown, about 20 minutes.
While baking, mix Manukora honey, red pepper flakes, and apple cider vinegar in a bowl to make the hot honey.
Remove tart from oven once golden and bubbly. Drizzle with hot honey and serve immediately.