Dice half the onion. In a skillet, heat 1 tbsp (15 mL) oil over medium heat and cook onion until caramelized, about 8 min.
Finely chop 2 tbsp (30 mL) sage and stir into the skillet along with the apple, walnuts, Italian seasoning and 1/4 tsp (1 mL) each salt and pepper. Cook until the apples have softened slightly, 2 to 3 min. Remove from heat and set aside to cool completely.
Mix the cooled apple-onion mixture with the bread pieces, parsley and egg yolk. Add 1/4 cup (60 mL) of the broth to moisten the stuffing so it just holds together. Set aside.
Preheat oven to 425°F (220°C). Place both turkey breasts, skin side down, on a cutting board. Cut horizontally into the thickest part of each breast (but do not cut through) so they open up like a book. Season each of the cut surfaces with the remainder of the salt and pepper.
Mould 2 cups (500 mL) of stuffing into a log; place in the middle of one side of the first breast. Fold the meat over to close and use kitchen twine to wrap and tie the rolled turkey in 3 or 4 places. Repeat with second breast.
Thinly slice the remaining onion and scatter in a roasting pan along with the remaining sage sprigs. Place the stuffed turkey breasts overtop and brush them with the remaining oil. Add the remaining broth to the pan and cook in centre of oven for 15 min. Reduce the heat to 375°F (190°C) and continue to cook for 40 min. or until the internal temperature reaches 165°F (74°C). Transfer turkey to a platter and let rest 5 to 10 min. Remove the twine, slice and serve with the onion and sage stuffing.