Heat 1 tablespoon neutral oil in a wide skillet. Add the chicken and cook for 12–15 minutes, breaking it up as it cooks, until browned and cooked through. Season with salt and transfer to a plate.
Sauté the vegetables:
Add 1 teaspoon neutral oil to the skillet. Add the shallot and bell pepper. Cook for 5–6 minutes, turning often, until they soften. Season lightly with salt.
Add the light parts of the bok choy, tomatoes, and jalapeńo. Sauté for 5 minutes. Add a pinch of salt.
Make the sauce:
Whisk together all the ingredients for the sauce. Taste and adjust according to your preference.
Finish the chicken:
Return the chicken to the skillet and toss to combine. Pour in the sauce and bring to a boil. Add the Thai basil leaves and the leafy green parts of the bok choy. Stir to combine. Reduce the heat to low and continue stirring for 2–4 minutes to reduce the sauce a bit. If the sauce reduces quickly, add a few splashes of water as needed. Taste and season. Turn off the heat.
To serve:
Spoon the chicken onto a serving platter and garnish with more Thai basil leaves. Enjoy!