Preheat the oven to 375 degrees F. Line a half-sheet pan with parchment paper and set aside.
Using a half-sheet pan as a guide, roll the Flaky Pastry Dough out to a bit larger than the sheet pan (13 by 18 inches). Trim the dough with a sharp knife and transfer to the prepared sheet pan (it should fit snugly). Refrigerate for 20 minutes to chill.
Dock the dough with a fork and bake until risen and golden brown on top, about 35 minutes. Set aside.
In a skillet, combine the olive oil, onions and garlic; saute over medium heat until the onions have softened, about 15 minutes. Add the maple syrup and paprika and stir to combine.
In the bowl of a food processor, combine the cream cheese, artichoke hearts, Parmigiano-Reggiano, mayonnaise, the onion mixture and salt and pepper to taste. Pulse until mostly smooth, with a few small artichoke pieces remaining.
Gently spread the artichoke mixture over the pastry, leaving a 1/2-inch border. Top with the sliced tomatoes. Bake until the edges of the filling are beginning to brown, about 15 minutes.
Top with the fresh herbs. Serve warm and immediately.
Add the flour and salt to a large bowl and stir to combine. Add the butter and toss to combine. With your fingers, begin to "smush" the butter into flat pieces. Continue smushing until all the butter is flattened but none of the pieces are larger than a quarter. The flour will look like coarse cornmeal.
Add the water, quickly folding it in with a wooden spoon to distribute the moisture. (Do not stir vigorously--the dough should appear shaggy.) Use your hands to break up any large clumps of moisture. Then use your knuckles or a palm to smear the dough up the sides of the bowl (a technique known as fraisage). This distributes the butter over a larger surface to achieve larger flakes and compact the dough. Once you've gone around the bowl one time, fold the dough over itself a few times to pick up any dry bits from the bottom. Gently press the dough into a disk. (Note: The dough should remain very cool to the touch throughout the process. If it approaches room temperature, refrigerate it for 5 to 10 minutes to chill.)
Transfer the dough to a lightly floured work surface and roll out to a 10-by-12-inch rectangle. Perform a letter fold by folding one of the short ends towards the middle and the other short end over the first, like folding a business letter.
Turn the dough 90 degrees, so the long side faces you, and perform a second letter fold. Turn the dough 90 degrees again; perform a third letter fold.
If the dough still feels cool, it can be used immediately. Otherwise, wrap it in plastic wrap and chill for at least 20 minutes. The dough can be refrigerated for up to 1 week or frozen for up to 1 month.