How to Make It
Prepare the salsa verde: Combine shallot, vinegar, capers, garlic, and anchovies in a bowl. Let stand 10 minutes. Stir in olive oil, parsley, cilantro, and tarragon; set aside.
Prepare the vegetables: Prepare a wood or charcoal grill. (See "Hearth-fired Hack," below.) Place eggplants, red bell pepper, yellow bell pepper, and scallions on a rimmed baking sheet. Drizzle with olive oil; toss to coat. Sprinkle with salt and pepper.
Place eggplants and bell peppers on oiled grill grate over direct heat; grill, uncovered and turning occasionally, until marked and charred, 2 to 3 minutes. Transfer eggplants and bell peppers to indirect heat, and grill, covered with grill lid, until just tender, 5 to 7 minutes. Transfer to a baking sheet; cover with aluminum foil to keep warm.
Place scallions on grill grate over direct heat; grill, uncovered, 1 minute; turn scallions. Grill, uncovered, until lightly charred and wilted, 1 to 2 minutes.
Roughly chop peppers and arrange on a platter with eggplant and scallions; top with dollops of burrata and salsa verde.