Adjust the oven rack to the middle position and heat the oven to 400°F. Line a baking sheet with parchment paper.

Roll the puff pastry into a 10-inch square on a lightly floured surface, then cut into four 5-inch squares. Score a 1/2-inch border around the edge of each square with a paring knife, being careful not to cut all the way through, and place them on the prepared baking sheet.

Heat the olive oil in a large skillet over medium-high heat until the oil shimmers. Add the artichokes, shallot, and salt, and cook until the artichokes are tender and show spotty brown patches, about 3 to 5 minutes.

Pour in the wine and simmer uncovered until the liquid has completely evaporated, about 3 minutes.

Stir in the balsamic vinegar and remove the skillet from the heat.

Divide the goat cheese evenly among the centers of the pastry squares, spreading it to the scored borders. Top the cheese with the artichoke mixture.

Bake until the pastry edges are puffed and deeply golden brown, about 15 minutes. Serve warm while the crust is still crisp.