In bowl, combine active dry yeast and 1/8 tsp. sugar with 2 tablespoons warm water, mixing until dissolved. Set aside on counter for 10 minutes.

Meanwhile, prepare vegetables. In small bowl, stir rice wine vinegar, water and sugar until dissolved. Fill one bowl with carrots, and another with cucumbers. Pour half the liquid over carrots and remaining over cucumbers. Set aside for 10 minutes, then remove excess water from carrots and cucumbers.

To create buns, whisk flour, remaining sugar, remaining warm water, baking powder, baking soda and salt. Add yeast mixture and mix until dough-like consistency forms.

Lightly dust counter with flour and place dough on surface. Knead until smooth, about 5 minutes. Transfer dough to greased bowl. Cover with clean damp dishcloth and rest dough for 1 hour.

While dough rests, prepare (9) 4x4-in. pieces of parchment paper squares.

Punch dough down to remove air and divide dough into (9) 40g pieces. Shape each piece into a smooth ball and roll into 1/4-in. thick ovals – make sure to smooth out other side. Length should be twice the size as it is wide. Brush top tightly with oil, fold oval in half and set on prepared parchment paper squares. Cover and proof buns for 30 minutes.

In the meantime, bring 2-3/4 cups water to boil. Insert steamer bowl in pot with buns inside, covered, and turn heat to medium-low. Steam buns for 10 minutes and remove from heat. Leave covered for 5 minutes before opening lid.

In pot on medium heat, preheat oil to 350 degrees F. Pour oat milk into bowl. In batches, dip sliced shiitake mushrooms in oat milk, remove and let excess liquid drip off. Dip into flour until evenly coated. Return to oat milk, then back into flour. Repeat with remaining mushrooms.

Transfer mushrooms to pot (in batches) and fry for 4 minutes each or until crispy and golden brown. Transfer to wire rack with paper towel under to catch any oil.

In small bowl, combine sauce ingredients.

Serve warm bao buns filled with vegetables, fried mushrooms, sauce, green onions and cilantro leaves.