Heat the oven to 400°F. In a roasting pan, combine the vegetables and ¼ cup of the olive oil. Roast until nicely caramelized on all sides, about 20 minutes. Add the tuna, anchovies, and capers; roast 10 minutes more.

Cool the roasted ingredients slightly; transfer to the bowl of a food processor. Add the remaining olive oil and the lemon juice. Puree to a smooth paste; add the mayonnaise and pulse to incorporate. The sauce should be creamy. Season with salt and pepper to taste.

Pool the tuna sauce onto individual serving plates. Arrange the turkey slices in a single layer on the sauce, leaving some sauce peeking out from the edges. Drizzle with additional sauce and garnish with the cornichons, parsley, and lemon wedges.