Preheat the oven to 425 degrees F.
Pour enough oil to coat the center of a baking sheet. Season the scored eggplant with salt and pepper, then arrange the cut sides down in the EVOO. Drizzle
with EVOO and season with salt and pepper. Wrap in a foil pouch and roast
along with the eggplant until very tender, 40 minutes. Cool to handle.
Heat 2 tablespoons EVOO, a couple of turns of the pan, in a Dutch oven
over medium-high heat. Add the thyme, chile
and salt and pepper and stir to soften, 5 minutes. Add the tomato paste
and stir 1 minute more. Then add the stock, wine
, and tomatoes
. Scrape the eggplant
away from skin and add the flesh, along with the garlic, squishing the cloves
from the skins. Add the basil. Puree the soup
with an immersion blender
to thicken. Cool and store for a make-ahead meal. Reheat the soup over medium heat, and top with the basil and cheese