In a large skillet over medium-high heat, heat 1 Tbsp. neutral oil until shimmering. Add onion, jalapeños, and ½ tsp. 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 ¾ tsp. 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 Tbsp. 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 Tbsp. beef filling and 1 Tbsp. 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 Tbsp. lime juice until smooth. Refrigerate until ready to serve.

Preheat oven to 400°. Brush tops of tortillas with oil. Bake taquitos, turning halfway through, until tortillas are crisp, golden, and beginning to brown, 18 to 20 minutes.

In a large, heavy skillet heat over medium-high heat, heat 2 cups oil until an instant-read or deep-fry thermometer registers 375°. Working in batches, fry taquitos, turning halfway through, until tortillas are crisp, 4 to 5 minutes.