Cook Rice: Add all rice ingredients to saucepan and cook according to time on package.
Make sauce: Combine sauce ingredients together in small saucepan and set aside.
Prepare Veggies 1: Heat oil over medium in a wok or large fry pan.
Sautee mushrooms and shallots for 5 minutes or until softened and most of mushroom liquid is cooked off. Stir occasionally.
Add garlic and sauté another 2 minutes, stirring frequently (add tiny amount of liquid if browning too much).
Add peas, salt, and pepper and cook for 2 minutes, stirring frequently.
Turn heat to med-low. Toss in herbs and heat through 1 minute. Turn off heat and cover with a cocked lid until ready to reheat lightly just before serving.
Prepare Veggies 2: Heat large cast iron skillet over medium heat until hot.
Add oil and heat a few seconds, add hearts of palm into a single layer and cook about 3 minutes until brown, flip them to other side.
Add zucchini chunks, salt, and pepper keeping everything in a single layer. Cook 3-4 more minutes until browned.
Put it all together: Turn Veggies 1 back on med heat and heat just until hot again, heat sauce over medium until steaming. To serve: place ¼ rice in bowl, top with ¼ Veggies 1 & 2 and ¼ sauce. Add a sprinkle of sesame seeds and basil leaf sprigs. Repeat for remaining bowls.