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Preheat grill/broiler to medium.
Using mandoline or sharp chef’s knife, cut zucchini and eggplant lengthwise into long strips, ¼-inch thick. Arrange on prepared baking sheets and lightly brush with olive oil.
Scatter thyme over vegetables and season generously with sea salt. Grill/broil 3 minutes, then flip and grill/broil another 3 minutes.
Watch carefully so they don’t burn. You may have to remove zucchini at this point and leave eggplant in another 1–2 minutes. Cook until vegetables are soft, but not falling apart. Once done, set aside to cool.
Combine 3 tablespoons olive oil, nuts, parmesan, tomato paste, sun-dried tomatoes, and cherry tomatoes in food processor and blitz until very smooth. Season with sea salt and pepper.
Take a strip of eggplant, layer on a strip of zucchini; then gently spread a layer of tomato mixture over it. Roll strip up and spear with a cocktail stick/toothpick, if necessary, to seal it closed.