In a small saucepan over medium heat, whisk together the sesame oil, soy sauce, brown sugar, 1 tablespoon of the vinegar, and the chili paste, tomato paste, and garlic. Bring to a low boil, then lower the heat to low and let simmer for 10 minutes. Remove the sauce from the heat and set aside.
In a medium-sized bowl, combine the carrot, daikon, and remaining 2 tablespoons of vinegar, toss thoroughly, and set aside.
Brush the steaks with the oil. In a skillet or grill over medium-high heat, grill each steak for 3 minutes per side.
Remove the steaks from the heat and cut each into strips. Toss the strips in the sauce, and return to the grill or skillet for another 2 to 3 minutes. Remove from the heat.
Lightly toast each piece of bread.
Spread the mayo on the inside of each piece of bread, then layer on the roast, cucumber, carrot mixture, jalapeño, and cilantro.
