Heat the oil in a medium saucepan over medium heat. Once the oil shimmers, add the carrot, celery, onion, fennel and garlic, stirring to coat. Cook for about 8 minutes or until the mixture begins to brown a little. Clear a small space at the center of the pan and add the tomato paste. Cook for a minute or two, then add the wine and stir to incorporate those ingredients, scraping up any browned bits from the bottom of the pan.

Cook until the liquid has reduced by half, then stir in the 3 cups seafood broth, the potatoes and corn. Cook for at least 20 minutes or until the liquid has reduced by half. The potatoes should be barely tender. Add the tarragon and basil, then season with salt and pepper to taste.

Stir in the cream; cook for 15 minutes or until the liquid has reduced by half, then stir in the lobster meat. Remove from the heat.

Preheat the oven to 400 degrees. Use cooking oil spray to grease a medium-size souffle dish. Place on a rimmed baking sheet. Cut the puff pastry to fit just inside the rim of the dish.

Pour the potpie mixture into the dish, then cover with the puff pastry, trimming off the excess. create an egg wash with 1 egg and about 1/4 cup of water; brush it onto the puff pastry and discard the rest. Use a sharp knife to create a small hole at the center of the pastry or cut a few slits in the top. Bake for 7 to 10 minutes, until golden brown.

Let the pot pie rest for 5 minutes before serving.