Cook pasta: In very well salted water until 1 to 2 minutes before doneness and drain.
Prepare eggplant: Trim eggplant and slice into 1/2-inch coins. Brush both sides with olive oil and sprinkle with salt and freshly ground black pepper. Heat grill to medium-high. Arrange eggplant in one layer and cook until charred underneath, about 8 minutes. (If it’s sticking to the grill, it wants to cook longer.) Flip pieces over and cook until charred on second side, about 5 to 8 minutes more. Set aside to cool slightly then chop into chunks.
No grill? Heat oven to 425. Trim eggplant and slice into 1/2-inch coins. Coat a baking sheet generously with olive oil, arrange eggplant on top and sprinkle with salt and pepper. Roast, without disturbing, for 15 to 20 minutes. Carefully flip each piece: the undersides should be blistery, dark and a bit puffy and should release easily; if they don’t want to, cook them a few minutes longer. Flip each piece, sprinkle again with salt and pepper, and roast on the second side for 10 to 12 minutes, or until charred underneath again.
Make dressing: In food processor, coarsely grind walnuts, cheese, garlic, thyme, salt and freshly ground black pepper and/or red pepper flakes. Stir in oil and tomatoes, then whisk in vinegar to taste.
Assemble salad: Toss cooked pasta with walnut dressing and additional vinegar and oil to loosen (I used about 1 tablespoon extra oil and 2 tablespoons extra vinegar in total). Add eggplant and toss again. Adjust seasonings to taste, then stir in cheese and herbs.