In a large ovenproof skillet, heat oil over medium-high heat; add butter. When butter begins to bubble, season chicken with salt and pepper; add to skillet. Cook for 4 minutes, turn chicken over, add pears and shallots, and place in a 425°F oven. Roast for 4 to 5 minutes or until chicken is no longer pink (170°F). Transfer chicken to a platter; keep warm.
Return skillet to oven and roast for 8 to 10 minutes more or until pears and shallots are just tender, shaking skillet occasionally. Transfer pears and shallots to platter with chicken. Reserve any pan juices.
Add pear nectar, hazelnut oil, and vinegar to skillet. Stir to combine and incorporate pan juices; transfer dressing to a large bowl. Coarsely chop chicken, pears, and shallots; add to dressing in bowl. Stir gently to combine and transfer to a serving platter. Top with blue cheese and hazelnuts. Serve warm with flat breads.