1. Prep marinade
Finely chop 1 teaspoon garlic. Pick mint leaves from stems and finely chop 2 teaspoons; keep remaining leaves whole. Into a large bowl, finely grate lime zest and squeeze 1 teaspoon lime juice. To bowl with lime zest and juice, add garlic, chopped mint, fish sauce and 1 tablespoon oil. Season to taste with salt and pepper.
2. Grill chicken
Heat a grill or grill pan over high. Pat chicken dry and drizzle lightly with oil. Add chicken to grill or grill pan and cook until charred in spots and cooked through, 2–3 minutes per side. Transfer chicken to bowl with marinade and let sit for at least 5 minutes, turning to evenly coat chicken in sauce.
3. Prep veggies
Meanwhile, peel carrots lengthwise into ribbons. Thinly slice cucumber into rounds. Transfer carrots, cucumbers, and whole mint leaves to a large bowl; toss with 1 tablespoon oil, 1 teaspoon vinegar, and a pinch each of salt and sugar. Let sit until step 5.
4. Make Sriracha mayo
Preheat broiler with a rack in the upper third. In a small bowl stir to combine mayo, Sriracha, and 1 teaspoon water. Slice baguettes in half lengthwise and lightly oil the cut sides. Transfer to broiler, cut side up, and cook until toasted, about 2 minutes (watch closely as broilers vary). Alternately, grill bread until charred and warmed through, 1—2 minutes.
Cut chicken into strips and return to bowl with marinade, toss to coat in accumulated juices. Spread some Sriracha mayo on bottom baguette half and layer on the pickled veggies and grilled chicken. Spoon remaining marinade and Sriracha mayo over top, and sandwich with top half of the baguette. Enjoy!