1. Combine the vinegar, 1 cup water, sugar, and 1/4 teaspoon salt in a medium bowl. Stir until the sugar is dissolved. Soak the carrots in the vinegar brine for at least 30 minutes.
2. Place the chicken breasts in a small saucepan with just enough water to cover. Add 1/4 cup soy sauce and 3 sprigs cilantro and bring to a simmer. Cover and simmer, about 18 minutes. Remove the pan from the heat, uncover, and cool the chicken in the liquid, about 30 minutes. Tear the chicken into shreds and toss with 1/3 cup mayonnaise, Sriracha, and the remaining 1 tablespoon soy sauce.
3. Preheat the oven to 375 degrees F. Slice the baguettes lengthwise, leaving a hinge intact. Spread mayonnaise on both sides of the bread. Add the chicken and toast, open faced, 5 to 8 minutes. Drain the carrots. Add the carrots, cucumbers, and cilantro leaves to each sandwich and serve immediately.
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