On a gently floured piece of parchment paper, roll out the chilled Pie Dough to a circle about 15 to 16 inches in diameter. Trim it to form an even 14-inch circle. Invert a sheet pan so the flat, bottom side is facing up. Lifting the parchment paper to lift the tart dough, transfer it to the sheet pan. Wrap the pan tightly with plastic wrap, and chill in the refrigerator for at least 30 minutes and up to 3 days.
In a small bowl, combine the softened chevre, egg yolk, heavy cream, 1/4 teaspoon kosher salt, and 1/8 teaspoon pepper, and stir until smooth. Set aside.
Cut the carrots, diagonally, into chunks about 2 to 3 inches in length and no wider than 1 inch, and transfer to a large bowl. Slice each onion half into 1/2-inch wide fans and add to the bowl. Toss the vegetables with the olive oil, 3/4 teaspoon kosher salt, and 1/8 teaspoon pepper, and set aside.
Remove the tart dough from the refrigerator, and using the back of a spoon or a spatula, spread the cheese mixture onto the dough, leaving a 1-inch border around the edges. Use your fingers to gently crimp the edges of the dough, creating a pleated freeform crust. Arrange the vegetables in the middle of the tart, making sure they are in one even layer that covers the cheese mixture beneath.
In a small bowl, lightly beat the egg white with a fork. Brush the tart edges with the beaten egg white and sprinkle with 1/4 teaspoon sea salt. Bake for 40 to 45 minutes, until the vegetables are deeply caramelized and the crust is a rich golden color, rotating the pan halfway through.
Remove the tart from the oven and let it cool slightly. Place the chicory leaves in a medium bowl, drizzle with the lemon juice, and toss gently. Sprinkle the herbs over the tart and arrange the chicory leaves on top, leaving a bit of the tart edges peeking through. Sprinkle with 1/2 teaspoon sea salt and serve.
Yield:1 (14-inch) pie crust
Place the flour, sugar and salt in the bowl of a food processor, and pulse once or twice to combine. Add the butter and pulse twice more, until the butter is in medium-sized pieces. Steadily pour the ice water into the machine while pulsing it as quickly as you can, until the butter is still visible in large smears and the dough is pushing up the sides of the bowl. It should look like damp bread crumbs. (You may not need to add all the water.)
Scrape the dough into a large bowl, cover, and refrigerate for at least 1 hour. (The dough will continue to hydrate, but if it still feels powdery and dry, wet your fingertips and flick a little cold water onto the crumbs.) After 1 hour, gently press the dough into a disc and wrap in plastic wrap. Chill for at least 1 hour more before rolling out.