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
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