Wash and dry the peppers, eggplant, and corn. Remove and discard the stems and seeds of the peppers; small dice the peppers. Slice the eggplant in half lengthwise, then into ½-inch-thick half moons. Cut the kernels off the cobs. Peel the shallot; slice half the shallot into rings; mince the remaining half.

In a large pan, heat 2 teaspoons of olive oil on medium-high until hot. Add the eggplant and salt and pepper. Cook, stirring occasionally, or until lightly browned. Add the garlic, sliced shallot, and diced peppers. Cook, stirring frequently, 1 to 2 minutes, until softened. Add the corn and cook 1 to 2 minute, stirring frequently. Taste and adjust seasoning and transfer to a bowl. Wipe out the pan.

While the vegetables cook, combine the softened butter with the minced shallot and tarragon, seasoning to taste with salt and pepper.

Pat the fish dry and season with salt and pepper. Heat the remaining 2 tablespoons olive oil on medium-high; when it shimmers, add the fish and cook, turning once, until just cooked through2 to 6 minutes per side depending on thickness of fish (see note below). Divide the vegetable mixture between two plates, top each with a piece of fish, and add a dollop of the shallot-tarragon butter to each. Serve hot.