Avoid the temptation to whiz the salsa verde ingredients in a blender—the rough texture that comes from hand chopping and pounding in a mortar and pestle is what you're looking for. Slideshow: More Grilled Vegetable Recipes
Using a mortar and pestle, pound and mash the anchovies and garlic to a paste. Stir in the vinegar, then add the oil in a slow stream, stirring constantly. Add the herbs, then season with salt and pepper. Set aside.
Light a grill or preheat a grill pan. Brush the eggplant and zucchini slices on both sides with the olive oil and season with salt and pepper. Grill the vegetables over moderate heat, turning once, until lightly charred and tender, 10 to 15 minutes.
Arrange the vegetables on a serving platter. Spoon some of the salsa verde over the vegetables, and serve the remaining sauce on the side.
The salsa verde can be made 3 hours ahead.