Peel and core the apples, then cut them into quarters.
Spread the butter on the bottom of a 12-inch ovensafe nonstick skillet. Mix the sugar, salt and vanilla together to evenly distribute the caviar. Sprinkle the sugar mixture evenly over the butter. Squeeze over the lemon juice.
Place the apple quarters cut-side up on top. Remember, the bottom will become the top so make it look pretty. Put the pan over medium heat and cook until the sugar melts, caramelizes and begins to thicken. The apples will release their juices during this process, so it could take 10 to 15 minutes. If the juices start getting too dark, lower the heat a little.
While the apples are cooking, take the puff pastry out of the fridge. Use a knife to cut a circle just big enough to fit over the top of the apples in the skillet. Keep chilled.
When the sugar has caramelized, place the pastry circle over the apples, gently tucking in the sides. Transfer to the oven and bake until the pastry is risen and golden brown, 15 to 20 minutes. Let rest 10 to 15 minutes.
Carefully turn the tarte tatin out onto a serving plate. Serve with whipped cream.