Slice off the top and bottom from the eggplant and peel. Slice into 1/2" slices, lightly salt, and place in a colander. Weight the eggplant down with some plates and let sit for 30 minutes. The salt can counter some bitterness frequently present in eggplant, and help remove moisture. Chop and set aside.
Heat up the olive oil in a saute pan over medium heat and add the onion and carrot. Once they become just tender, about 8 - 10 minutes, add the thyme, pepper flakes, salt and pepper. Saute for another couple of minutes to open up the herbs and spices, and add the tofu. Saute for another couple of minutes.
Add the eggplant, tomatoes, capers, and vegetable broth. Simmer for 20 minutes or until the tomatoes break down and melt into the sauce. Add the balsamic vinegar and stir. Simmer for another minute.
Bring a large pot of salted water to a boil and cook the pasta according to the package directions.
Toss the pasta and sauce together and serve with Parmesan cheese on the side.