Heat 1 tablespoon of the oil in a large skillet over high heat. Add half the beef and cook, breaking it up with a spoon, until browned on all sides but not completely cooked through, 4 to 6 minutes. Transfer to a medium bowl, leaving as much fat in the skillet as possible. Repeat with the remaining beef.
Reduce the heat to medium and add the garlic, carrots, jalapeno, onions, poblano, potato, 4 teaspoons salt and 1/2 teaspoon pepper. Cook, stirring, until the vegetables are tender but not browned, 10 to 12 minutes. Clear a space in the pan and add the tomato paste, chili powder and cumin and cook, stirring, until fragrant, about 1 minute. Stir to bring the whole mixture together, then add the stock and reserved beef along with any accumulated juices to the skillet. Bring to a simmer and cook, stirring and scraping up any brown bits from the bottom, until the liquid has evaporated, about 20 minutes. If necessary, season with salt and pepper.
While the picadillo is cooking, pour oil into a large Dutch oven or heavy-bottomed pot to come 3 inches up the sides and fit with a deep-fry thermometer. Heat over high heat until the thermometer registers 375 degrees F.
Holding a tortilla perpendicular to the oil near the edge of the pot, carefully lower into the oil so that the tortilla slides to the bottom (this method will fry and seal both sides of the tortilla, allowing steam to inflate—or "puff"—the tortilla like a balloon). After a few seconds, the puffy tortilla will float to the surface; turn it over and push the top edge of a metal spatula (a fish spatula works best) into the center of the tortilla, bending it into a taco shape, and press it below the oil's surface. Hold it in place and cook until golden brown and crisp, about 1 minute. Invert the taco shell onto paper towels to drain. Repeat with the remaining tortillas.
Spoon the beef picadillo into the puffy taco shells. Top with lettuce, salsa, cheese, cilantro and onion. Serve with lime wedges.