Preheat the oven to 375ºF.
Arrange the eggplant in a single layer in a 9”x13” glass or ceramic baking dish (like Pyrex). Sprinkle with the coarse salt and let stand until you see tiny moisture bubbles on the surface, 10 to 15 minutes. (This draws out the eggplant’s excess moisture and bitterness.)
Pat the eggplant dry with paper towels. Toss with 1 tablespoon of the oil. Cover tightly with foil and roast until the eggplant is starting to soften, about 25 minutes. Then add the tomatoes and remaining tablespoon of oil, and toss to combine. Continue roasting, uncovered, until the vegetables are soft and golden brown, about 25 minutes more.
Meanwhile, make the pesto. In a food processor, combine the basil, garlic, seeds, and miso. Pulse until everything is broken down. With the motor running, gradually stream in the oil and lemon juice, and season with salt and pepper. Puree until smooth. Taste and adjust the seasonings, if needed.
Transfer the vegetables to a serving platter and dollop with the pesto. Serve warm or at room temperature.
