Heat 2 tablespoons vegetable oil in a large nonstick skillet over medium-high heat. Working in batches, fry the tortilla strips, flipping, until golden, about 2 minutes. Transfer to a paper towel-lined plate using a slotted spoon. Sprinkle with 1/2 teaspoon taco seasoning.
Add the remaining 1 tablespoon vegetable oil to the skillet. Add the red onion and cook, stirring occasionally, until just tender, about 3 minutes. Add the beef, garlic and the remaining 2 teaspoons taco seasoning. Cook, breaking up the beef with a spatula, until no longer pink, about 3 minutes. Add the tomatoes and pickled jalapenos with carrots and onions; cook until the tomatoes are slightly softened, about 3 minutes. Remove from the heat and stir in the cilantro.
Mix the sour cream with the jalapeno brine in a small bowl. Divide the lettuce among bowls; top with the beef mixture, cheese, sour cream and tortilla strips.