Season the chopped chicken cubes with salt and pepper. In a pan or skillet, heat 2 tablespoons of the olive oil on medium-high until hot. Add the chicken and cook, stirring occasionally, 6 to 8 minutes, or until browned and cooked through. Leaving the browned bits in the pan or skillet, transfer the chicken to a plate.
While the chicken cooks, in a medium bowl, whisk together the Blue Apron sushi sauce (or soy sauce), sweet chili sauce, vinegar and water.
Add the remaining 1 tablespoon of olive oil to the pan or skillet; heat on medium-high until hot. Add the celery, ginger, peppers and the white bottoms of the scallions. Cook, stirring frequently, 1 to 2 minutes, or until softened and fragrant.
Add the chopped bok choy, cook for 30 seconds to 1 minute, or until the leaves are wilted. Add the cooked chicken and the sauce to the pan or skillet. Cook, stirring frequently, until well combined. Add the noodles, cook and stirring frequently, 3 to 4 minutes, or until thoroughly heated through.
Turn off the heat and season with salt and black pepper to taste. Serve the dish with chopped cashew and the sliced green tops of the scallions.