Carrot Tatin

Name: Carrot Tatin
Ingredients: 12.35 oz (about 2.5 cups) all-purpose flour; 1 oz (about ⅓ cup) sugar; 3.5 oz (about ¾ cup) unsalted butter, softened; 0.07 oz (about ½ teaspoon) salt; 1 large egg; 2.2 lbs (about 1 kg) Nantes carrots; 7 oz (about 1 cup) unsalted butter; 4.4 lbs (about 2 kg) Nantes carrots; 2 shallots; 7 oz (about ½ cup) unsalted butter; White stock (enough to cover the carrots); 1 sprig of thyme; Salt to taste; 7 oz (about ¾ cup) sherry vinegar; 14 oz (about 1.75 cups) olive oil; 1 bunch chervil; 1 bunch carrot tops (greens); Salt and pepper to taste