Preheat the oven to 350 degrees F. Meanwhile, pickle the carrot: In a pint-size jar, combine carrot, vinegar, sugar, and 1 teaspoon of salt. Cover and shake to dissolve the sugar and salt.
Place salmon fillets on a foil-lined baking sheet. Drizzle with 1 tablespoon of olive oil. Place in oven and bake until just cooked through and flaky, about ten to twelve minutes.
Whisk together lime juice, mayonnaise, and chili paste to make a dressing.
Place the tortilla on a plate. Spread the mayo in the middle of the tortilla, leaving a 1-inch border. Arrange the salmon, cabbage, carrots, cucumber, scallion, cilantro, mint, and jalapeño in a line on one end of the wrap, leaving a 1-inch border. Fold in the sides of the tortilla and tightly roll it up.