Pre-heat oven to 400 degrees Fahrenheit and line a baking sheet with parchment paper.
Unroll thawed puff pastry and lightly flour a rolling pin and gently roll the puff pastry so it's a bit thinner.
Use a sharp pairing knife to score a half inch boarder around the puff pastry, leaving a crust and use a fork to dock holes in the middle of the pastry. This will help it not puff up as it cooks.
Place pastry on lined baking sheet and pre-cook the puff pastry for 10 minutes to give it a head start. Once done, remove from oven and set aside.
Heat a skillet over medium heat and drizzle in olive oil. Add chopped shallots and saute for 2-3 minutes until shallots just begin to soften. Then add in the garlic and cook for another minute.
Add in chard leaves, in batches if needed and saute until just wilted.
Pour in heavy cream and grated Parmesan and give everything a good stir. Turn off heat and set aside.
Once pastry is cool enough to handle, spoon the chard mixture onto the puff pastry, leaving a boarder and into an even layer.
Bake tart for another 15 minutes until pastry has puffed up and is lightly golden brown.
Once done, remove from oven and garnish with grated Parmesan cheese, shavings of ricotta salata and sprinkle of sumac. Cut into squares and serve.