Roll out the puff pastry and fit it snuggly in a 23 centimeter fluted tart pan, ensuring it goes up the sides all the way. Prick the bottom of the puff with a fork and bake for 18-20 minutes. If the shell begins to rise in the middle while baking simply use a fork to release the air. Remove tart shell from the oven and let cool. Increase the oven temperature to 400°.
Meanwhile, in a medium sized mixing bowl combine 1-1/2 cups gruyere, mascarpone, Dijon, paprika, thyme, salt and pepper. Spread cheese mixture on the bottom of the tart shell.
Cover the cheese layer with the thinly sliced potatoes, alternating between the sweet potatoes, blue potatoes, yellow potatoes and red onion in concentric circles. Drizzle with olive oil and top with parmesan and a bit more gruyere.
Return to the oven and bake for an additional 20 minutes or until the potatoes begin to crisp up.