Heat 1 teaspoon oil and 1 teaspoon sesame oil over medium-high heat in a large skillet or wok. Add chicken and season with salt, and pepper. Cook one minute. Add 1 Tbsp butter, 1 Tbsp soy sauce and garlic to skillet and sauté, until cooked through. set aside and cover with foil.
In the same pan, heat half the oils for vegetables. Add half of the vegetables. Cook on high for 1 minutes. Add 1/2 Tbsp butter, 1 Tbsp soy sauce, and salt and pepper. Sauté until fork-tender—do not overcook. Set aside, and repeat steps with remaining vegetables.
Serve chicken and vegetables over rice, with sauce on the side for dipping.
For the sauce:
Mix all ingredients together and whisk until well combined.
Refrigerate overnight or at least for 8 hours prior to serving.
Yum Yum Sauce can be made ahead and stored in the refrigerator for up to one week.