Cut the chicken into 2" pieces. Add an egg, cornstarch, baking soda, and 3 ounces water. Use your hands to mix it all togehter until smooth. Add the oil and mix to combine. Refrigerate for 30 minutes.
In a large pan or cast iron skillet, heat 2 inches of high smoke point oil (like peanut oil) until it reaches 375°F. Place some paper towels under a wire rack, to put the chicken on when it's done.
Add the chicken pieces, one by one so they don't stick together. Don't crowd the pan. Cook the chicken in batches if it doesn't fit well. Cook for 1 minute. Using a slotted spoon, transfer the chicken to the wire rack. Let cool for 3 minutes.
Now heat the oil to 425°F. Transfer the chicken back to the oil and cook for 1 more minute, then again transfer the chicken to the wire rack.
To cook the broccoli, set a steamer basket inside a pot with 2 inches of water and a pinch of salt. Once boiling, add the broccoli florets and cover the pan. Let cook for 1 minute, then remove from the water.
To make the sauce, get a wok or large skillet and heat 2 tablespoons of oil over medium-high. Add the chilies and cook until fragrant, about 1 minute. Then add the garlic and cook until fragrant, about 1 more minute. Stir in the ketchup, oyster sauce, soy sauces, and chicken broth. Bring to a boil and reduce the heat to a simmer. Cook for 2 minutes.
Pour in the cornstarch slurry and stir until thickened. Stir in the sugar until dissolved, then add the vinegar.
Add the chicken pieces back to the wok with the sauce. Toss to coat. Serve over broccoli.