In a large skillet, heat oil until shimmery on medium heat. Add carrots, celery, onion, bay leaves, and thyme. Sauté vegetables until they begin to soften, about 5 minutes. Remove bay leaves.
Add chicken or turkey stock, chopped turkey, peas, and Boursin Pepper cheese and stir to combine. Season to taste with salt and pepper.
Transfer mixture to a 4-cup soufflé dish or ovenproof tureen. Spoon mashed potatoes over top and dust with smoked paprika. Place dish on a baking sheet and bake 15 minutes, until top is golden brown and filling is bubbly.