Preheat the oven to 400 degrees F and line a rimmed baking sheet with parchment paper.
Add the goat cheese, ricotta and 2 eggs to the bowl of a food processor fitted with the blade attachment. Pulse until the mixture is evenly combined. Next, add the Parmesan, parsley, chives, dill, lemon zest, garlic, 1/2 teaspoon salt and 1/4 teaspoon pepper. Pulse once again to combine all the ingredients. The mixture may look slightly liquidy, but once it bakes the egg will help stabilize the cheese mixture. Set aside.
On a separate rimmed baking sheet, toss the asparagus with the olive oil, 1/4 teaspoon salt and 1/4 teaspoon pepper. Set aside.
Unroll the puff pastry on a lightly floured work space and dust a rolling pin lightly with flour. Roll the puff pastry out to a 13-by-11-inch rectangle. Add the goat cheese-herb mixture to the puff pastry and spread it out into an even layer, leaving a 1-inch border all the way around the puff pastry. Nestle in the asparagus into the cheese mixture, alternating directions.
To make the egg wash, whisk the remaining egg with a splash of water. Use a pastry brush to brush the exposed crust all the way around the edges.
Transfer the tart to the oven and bake until the crust is golden and the cheese mixture is set, 25 to 30 minutes
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