Preheat your grill or broiler to high heat.
Roast the eggplants and red bell peppers, whole, as close as possible to the heat source, turning and rotating each piece with kitchen tongs, to achieve an evenly charred exterior. The skin on the eggplants should get a dark toasted color and the bell peppers should be charred with papery layer of black. Put the roasted vegetables in a glass bowl, cover with a kitchen towel and set aside to cool.
Once the reserved vegetables are cool enough to handle, peel both the peppers and eggplants. Slice the eggplants into long strips. De-seed the peppers and slice them into long strips.
Combine the peppers and eggplants in a bowl and add 2 to 3 tablespoons olive oil, salt and garlic, if using. Be careful to not over-season with salt because the anchovies are also very salty. Let stand for a minimum of 30 minutes.
Serve in individual plates or on a platter, family-style. Lay the anchovies across the top of the dish. Finish the dish with a final drizzle of olive oil, a small splash of sherry vinegar and a light sprinkling of sea salt, if using. Serve with grilled crusty bread and some black olives.