Position a rack in the center of the oven and preheat to 450 degrees . Thinly slice the potatoes. Place on a rimmed baking sheet with the green beans, anchovies, shallot and garlic. Drizzle with EVOO; season with salt and pepper.
Using a food processor, pulse the olives into a thick paste.
Season the fish or chicken, then slather with the olive paste. Set on top of the vegetables. Top each piece with a shingled layer of the tomatoes. Sprinkle the herbes de provence on top. Roast until cooked through, about 15 minutes for fish or 20 minutes for chicken.
Top the roasted fish or chicken and veggies with the cheese and parsley. Pass the warm baguette and butter at the table.