Preheat the oven to 350F and place parchment paper on two baking sheets.
Divide the puff pastry into 2 equal pieces and roll them out in oblong shapes, adding a bit of flour to your surface and rolling pin as needed to keep it from sticking.
Place the puff pastry on the parchment-lined baking sheets, drop 1 to 2 Tablespoons of the hot pepper jelly on the pastry and use the back of the spoon to spread it evenly. Bake for about 15 minutes or until golden brown. Remove from the oven and let cool a bit.
Arrange the apple slices on the pastry, top with the grated cheese and return the pastry to oven and bake for another 10 to 15 minutes or until the cheese is melted and golden brown.
Remove from the oven, sprinkle with the chopped chives and a few grinds of pepper. Let cool and then slice into fingers that are easy for people to pick up from an appetizer plate.