Mix the ingredients for the sauce together in a bowl and set aside. Chop the red bell pepper into 1/2 inch pieces. Slice the green onions and roughly chop the peanuts.
In a large bowl, whisk together the egg, 2 Tbsp of cornstarch, and a pinch of pepper until smooth. Cut the chicken breast into small, 1/2 inch cubes and toss to coat in the egg mixture.
Heat the vegetable oil in a large skillet over medium high heat until it is very hot, but not smoking (the oil should look wavy on the surface). To test whether or not the oil is hot enough, drop a bit of the egg mixture into the skillet. It should poof up and bubble furiously. Once the oil is very hot, add the egg coated chicken. Spread it out in the skillet and let it cook until golden brown on the bottom. Once golden, break up the pieces and flip them over. Cook a few minutes longer, or until golden on all sides and cooked through. Remove the cooked chicken from the skillet.
Add the frozen broccoli florets to the hot skillet and cook for just a few minutes, or until it is mostly warmed through. Add the chopped bell pepper and cook for one to two minutes more, or just until the raw edge has been taken off (it should still be fairly crisp).
Finally, add the chicken back to the skillet, along with the prepared sauce. Stir the skillet until everything is coated in the sauce and the sauce has become thick and bubbly (the heat should remain on medium-high). Stir in the chopped peanuts and sprinkle the sliced green onions over top. Serve with rice.