Remove the escargots from the can and drain well. Put them in a large bowl, fill with cool water, and drain, then rinse again in cool water. Drain well and return to the bowl. Set aside.
In a medium-size saucepan over medium heat, combine the wine, shallots, 1 tablespoon of the garlic, the thyme, bay leaves, 1/4 teaspoon of the salt, and 1/8 teaspoon of the black pepper.
Bring to a boil and let boil for 5 minutes. Remove the bay leaves and pour the mixture over the escargots and let stand at room temperature until completely cool.
Drain off 1/2 cup of the wine mixture and reserve. Cover and refrigerate the escargots if not using immediately.
Preheat the oven to 350 degrees F.
With an electric mixer set on low speed, beat the butter until smooth in a small mixing bowl. Add the remaining 2 tablespoons garlic and the parsley and beat to mix.
Add the reserved wine mixture and beat until incorporated. Add the remaining 1/8 teaspoon salt and 1/8 teaspoon black pepper and beat to mix.
Put 8 or 9 escargots in each of 8 (8-ounce) ramekins. Put 2 heaping tablespoons of the butter mixture over the escargots in each ramekin.
Cut 8 (4-inch) rounds out of the puff pastry with a knife and cover the top of each ramekin with a pastry round. With your fingers, press the pastry firmly over the rims and remove any excess. Lightly brush the pastry with the beaten egg.
Place the ramekins on a baking sheet and bake on the middle rack of the oven until the pastry is golden and puffed, 18 to 20 minutes.
Remove from the oven and let cool slightly before serving.