Preheat the oven to 400 degrees F (200 degrees C).

Bring a large pot of lightly salted water to a boil. Cook gnocchi in the boiling water until they float to the top, 2 to 4 minutes. Drain and set aside.

Toss chicken, peanut butter, curry paste, 3 tablespoons olive oil, honey, and salt together in a large bowl using your hands.

Combine broccoli, red onion, and remaining 2 tablespoons olive oil in a separate bowl until well coated.

Place chicken in a roasting dish; add broccoli mixture and gnocchi.

Bake in the preheated oven until chicken is no longer pink and juices run clear, about 30 minutes, stirring halfway. An instant-read thermometer should read at least 165 degrees F (74 degrees C).