Mix together soy sauce, 2 tablespoons rice vinegar, sesame oil, brown sugar, garlic, and ginger until well combined. Add pink oyster mushrooms and marinate for 30 minutes.
While mushrooms are marinating, mix together 1/4 cup of rice wine vinegar and 2 tablespoons of sugar, and salt until salt and sugar dissolve. Add carrots and cucumber and allow the mixture to set for at least 15 minutes.
Mix together the desired amount of Sriracha into vegan mayonaise.
Heat skillet over medium heat and add a splash of oil. Add the mushrooms, reserving the marinade. Sauté the mushrooms for about 5 minutes, stirring occasionally until they are cooked through and slightly caramelized. Pour in the reserved marinade and cook for an additional 1-2 minutes until the sauce thickens slightly. Remove from heat.
To assemble the sandwich, slice the mini baguettes or French rolls horizontally, leaving one side intact. Spread a generous amount of Sriracha mayo on both sides of the bread. Arrange a layer of pickled vegetables on the bottom half of the bread. Top with mushrooms and garnish with cilantro sprigs. Serve with lime wedges.
