Preheat oven to 400 °F (205 °C).
In a bowl, mix the ingredients for the sauce. Set aside.
Pat the duck breasts dry with paper towels. Remove excess fat from the breasts.
Using a knife, score the skin of the breasts in a crosshatch, making sure not to cut into the flesh. Season with Chinese five-spice, then with salt and pepper.
In a large pan, cook the duck breasts for 5 to 7 minutes over low-medium heat, skin side down, removing excess fat from the pan as you go.
Turn the breasts over and continue cooking for 1 to 2 minutes over medium-high heat.
Turn the breasts over so that they are skin side down again. Place the pan in the oven and cook for 7 to 8 minutes, until the internal temperature of the breasts reaches 136 ° F (58 °C) on a cooking thermometer. Remove from oven.
Place the breasts on a cutting board. Cover loosely with aluminum foil and let sit for 5 minutes before slicing.
Remove excess fat from the pan, then pour the reserved sauce. Bring to a boil and simmer for 4 to 5 minutes over low-medium heat, until the sauce becomes syrupy.
Meanwhile, heat the sesame oil in another large pan. Cook carrots, sugar snap peas, green onions and bell peppers for 2 to 3 minutes.
Pour honey and teriyaki sauce into the pan. Season with pepper and continue cooking for 1 to 2 minutes while stirring.
Serve duck breasts with vegetables and cover with sauce.
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