Prepare a gas or charcoal grill or firepit for medium-high heat.
Place the tomatoes in a large bowl. Add 1 tablespoon of the olive oil, season well with salt and pepper and toss gently. Arrange the tomatoes, cut side down, on the grill just until they develop grill marks, 2 to 3 minutes. Don’t overcook them.
Turn the tomatoes and cook for 2 to 3 minutes more. Use tongs to transfer them to a large bowl.
Add the eggplant to the same bowl you tossed the tomatoes in. Pour in another tablespoon of the olive oil and season well with salt and pepper. Toss the eggplant to coat in oil.
Grill the eggplant, turning often, until golden and tender, 10 to 12 minutes. Add to the bowl with the tomatoes.
Finally, plunk the beans into the same large mixing bowl, add the remaining olive oil and season well with salt and pepper. Toss the beans well and lay them carefully on the grill (don’t let them fall through the cracks). Grill, turning often, until nicely charred, 8 to 10 minutes. Use tongs to transfer them to the bowl of eggplant and tomatoes.
Spoon some of the dressing over the warm veggies. Give a quick toss and season to taste.
Stir in the red onion, dill, basil, and parsley. Add the remaining dressing and serve warm or at room temperature.