Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper. Lightly flour the work surface and roll out the puff pastry to a 9- by 12-inch even rectangle. Transfer to the prepared baking sheet. Combine the mascarpone, 1 1/4 teaspoons of the salt, the flour, egg and lemon zest, and then fold in the chives and tarragon. Spread over the puff pastry, leaving a 3/4-inch border. Make small cuts around the border about 1 inch apart with the tip of a paring knife.
Toss the asparagus with the olive oil in a bowl. Lay half of the asparagus in a neat row across the surface of the tart so the tips meet the edge. Do the same in the opposite direction with the remaining asparagus. Season with the remaining 1/4 teaspoon salt and some pepper. Bake until the border of the tart is deep golden and puffed and the top is lightly spotted golden brown, about 25 minutes. Let cool for 5 to 10 minutes and serve.
Serve with lightly dressed greens.