In a large skillet over medium-high heat, heat 1 tablespoon neutral oil until shimmering. Add onion, jalapeños, and 1/2 teaspoon salt and cook, stirring occasionally, until onion begins to soften, about 5 minutes.
Add garlic and cook, stirring, until fragrant, about 1 minute. Add tomato paste and stir to coat. Cook, stirring frequently, until paste starts to caramelize, 2 to 3 minutes.
Add ground beef, taco seasoning, and 3/4 teaspoon salt. Cook, breaking up meat with a wooden spoon, until no longer pink, about 5 minutes. Let cool slightly.
In a small bowl, toss cheddar and pepper Jack cheeses. In another small bowl, whisk flour and 4 tablespoons lime juice until smooth.
Wrap 5 tortillas in a damp paper towel or kitchen towel and microwave until softened and pliable, 40 to 45 seconds. Working one at a time, fill each tortilla with 2 tablespoons beef filling and 1 tablespoon cheese mixture.
Tightly roll 1 tortilla three-quarters of the way; brush remaining exposed tortilla with some flour mixture, then continue to roll to enclose. Arrange on a sheet tray. Repeat with remaining tortillas, filling, and cheese.
In a small bowl, combine stir sour cream, cilantro, a pinch of salt, and remaining 2 tablespoons lime juice until smooth. Refrigerate until ready to serve.
Make Ahead: Taquitos can be assembled (but not cooked) 4 months ahead. Freeze uncooked taquitos on sheet tray until they hold their shape and stay rolled, about 1 hour.
Transfer to a freezer-safe zip-top bag or airtight container and continue to freeze.
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