Preheat oven to 425°F and line a baking sheet with parchment paper.
Roll the puff pastry out a little to stretch it and then transfer to the baking sheet. Brush the edges of the pasty with the beaten egg.
Take the second sheet of pastry and cut 4 (1/2 inch) wide strips. Stick the strips around the edges of the big pastry sheet with the egg, then sprinkle with sesame seeds and black pepper. Prick the inside of the pastry all over with a fork.
Working inside the borders, arrange the peppercinis, basil, thyme, garlic, lemon zest, and chili flakes on the pastry. Then evenly sprinkle the Cypress and Fontina cheese over the top. Add the artichokes and lightly drizzle over a squeeze of honey. Chill in the freezer for 10 minutes.
Bake for 25-30 minutes or until the pastry is golden and the cheeses are melted.