In a large mixing bowl, whisk together the bao flour and sugar. Dissolve the dry yeast in 3 tbsp of the warm water and add to the bowl with the oil. Add the remaining water and knead for about 5 minutes, or until you get a smooth dough. It should have the texture of pizza dough and be very slightly sticky. Place in a bowl, cover with a wet kitchen towel and let it proof for about 90 minutes in a warm place.
Once the dough has almost doubled in size, transfer to a silpat or working surface slightly floured. Knead again and then divide into 4 balls. Flatten each ball using a rolling pin into an oval shape of a bit less than 1/4-inch. Brush each oval with oil and then fold in half. Place each one on a small piece of parchment paper. Let rise for another 20 minutes.
Bring a pot of water to a boil. Depending on the size of your bamboo steamer basket, place 2 or 4 buns inside. Be aware they will expand, so leave about 2-inch between each one.
Close your bamboo steamer basked with the lid and place it on top of the pot of boiling water. Steam for about 20 minutes. Remove from heat and let cool for 10 minutes.
Wash and rinse the kale. Add it to a blender with the rest of the ingredients. Blend on high-speed for about 30 seconds, or until everything is finely chopped and combined. Taste and adjust saltiness and sourness if needed. Transfer to a bowl and set aside.
To a small bowl, add the white vinegar, water, sugar, and salt. Stir to combine. Add the carrot sticks and let marinate for at least 1 hour. You can prepare it up to 3 days ahead and keep in the refrigerator.
Slice your tofu into 4 thin slices (about 1/2-inch). Add the cornstarch to a plate and coat each slice with cornstarch. Shake to remove excess.
Heat the oil in a non-stick pan over medium heat. Once hot, add the tofu slices and fry for about 5 minutes on each side, or until golden brown. Remove from heat and transfer to a plate lined with a kitchen paper towel to absorb excess oil.
Clean your pan with a kitchen paper towel, leaving about 1 tsp of oil. Heat over medium heat and add the tofu back to the pan with the soy sauce, maple syrup, and saté. Cook for about 3 minutes, stirring regularly to make sure the tofu absorbs the sauce. Remove from heat.
Heat the oil in a skillet over medium heat. Once hot, add the sliced mushrooms and sautée for about 5 minutes, or until cooked. Deglaze with soy sauce, add the ground black pepper and cook for another 1-2 minutes. Remove from heat and transfer to a small bowl.
Take one bun and open it to the 3/4. Spread about 2 tbsp of the kale pesto on the inside. Add a slice of saté tofu, a few slices of mushrooms, carrots, cucumber, and some cilantro. You can also add some slices of raw onions and toasted pine nuts. Transfer to a plate and repeat with the remaining buns. If your buns don't stay open, use a toothpick to keep everything in place. Serve immediately!
For warm bao, you can steam for about 1 minute in the bamboo steamer basket. These are best served the same day, but can be kept in the refrigerator for another day and reheated in a steamer.
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