Rich, buttery puff pastry offsets the the slightly sour flavor of the sorrel.
In a heavy, deep saucepan, melt butter over medium-low heat. Add onions. Cook, stirring frequently, until onions are soft and translucent, about 15 minutes.
Remove and discard the tough center ribs from the sorrel leaves. Bring a large stockpot of water to a boil, and add 2 teaspoons salt. Add sorrel, and cook just until the leaves wilt, 1 to 2 minutes. Drain sorrel in a colander, let cool, and squeeze out any excess liquid.
Add sorrel, the remaining teaspoon salt, and the pepper to the onions; cook over low heat until mixture breaks down and is almost soupy, about 20 minutes. Remove from heat, and let cool.
Preheat oven to 400 degrees. Line two baking sheets with parchment. On a lightly floured surface, roll one sheet of puff pastry into a 7-by-11-inch rectangle, about 1/8 inch thick. Transfer the dough to one of the parchment-lined baking sheets, and chill in refrigerator 30 minutes. Repeat process with the second sheet of puff pastry. Remove both sheets of puff pastry from the refrigerator. Using a sharp knife, score a 1/2-inch border around perimeter of each sheet, creating a picture-frame look. Using a fork, prick the entire surface within the scored edges on each sheet. Make an egg glaze: In a small bowl, combine 1 egg yolk and 2 tablespoons heavy cream; carefully brush egg glaze onto the borders.
Transfer both sheets of dough to oven, and bake until pastry has puffed up and is golden brown, about 15 minutes. Remove pastry from oven, and transfer to a wire rack to cool.
Add the remaining egg yolk and remaining 2 tablespoons cream to the sorrel mixture, and stir to combine. Divide the filling in two, and spread one half over each puff pastry. Return the tarts to the oven, and bake until the filling is hot throughout, about 20 minutes. Remove the tarts from the oven, and transfer to a wire rack to cool, about 10 minutes. Cut tarts into 2-inch squares, and serve warm.
Sorrel is a tender sour green with a clean, refreshing taste. If sorrel is unavailable, spinach makes a good substitute.