Slice eggplant in half, and cut into thin diagonal half moons. Then, cut the half moons in half to make a triangular shape.
Cut tofu into long, thin slices. Dry well by blotting.
Toss eggplant and 1/4 cup sesame oil in one mixing bowl. Toss tofu with 1/4 cup sesame oil in another bowl.
Cut the broccoli into very small florets.
Make sauce by whisking vinegar, soy sauce, fish sauce, date syrup and 1/4 cup sesame oil together.
Get cast-iron skillet hot, and lay eggplant slices down in a circular pattern. Layer eggplant slices on top. Let eggplant char on one side - about 2 minutes on the skillet.
Move eggplant around so different slices are on the bottom. Let char again for 2 minutes. Add a touch more sesame oil if its seeming dry.
Remove eggplant and set aside - it will be added back to the skillet.
Add tofu to pan, in one layer if you can. Char the tofu for 3-4 minutes on one side. Stir tofu and turn heat to medium, char for another 3-4 minutes. (This seems like a lot of work when you could just toss it all in together, but it makes a difference! )
Add small broccoli florets and eggplant slices, stir all together.
Add 1/2 the sauce, stir and cook for another 4 minutes, until broccoli is firm but tender and eggplant is soft and succulent.
Taste - the amount of sauce will vary depending on the size of your eggplant and broccoli heads. Add more if you think it needs it.
Sprinkle generously with shichimi togarishi and serve over rice.
* Optional substitution:
Other Asian chili spice blend, or white/black sesame seeds + aleppo chile flakes.