1. Preheat the oven to 400°. In a small bowl, toss the carrots with the rice vinegar and sugar and let stand for 10 minutes; drain.
2. In a small bowl, whisk the mayonnaise with the Tabasco, tomato paste and garlic and season with salt and pepper.
3. Form the meat into four 6-inch-long oval patties, about 1 inch thick. Season with the curry powder and salt and pepper. In a large skillet, heat the oil until shimmering. Cook the patties over moderate heat, turning once, until medium, about 12 minutes.
4. Meanwhile, spread the butter on the cut sides of the baguette. Set the bread cut side up on a baking sheet and bake for about 5 minutes, until lightly toasted. Spread the Tabasco-spiked mayonnaise on the bread and top each baguette section with a burger patty, pickled shredded carrots, pickled jalapeño slices and cilantro sprigs. Close the sandwiches and serve hot.