Adjust the oven rack to the middle position and heat oven to 400°. Stir together water and baking soda in a large bowl. Add beef and mix until thoroughly combined. Set aside.

Heat 1 tablespoon oil in a 12-inch skillet over medium heat until shimmering. Add onion and cook, stirring occasionally, until softened, 4-6 minutes. Add chile powder, paprika, cumin, garlic powder and salt and cook, stirring frequently, until fragrant, about 1 minute. Stir in tomato paste and cook until paste is rust-colored, 1 to 2 minutes. Add beef and cook, using a wooden spoon to break meat into pieces not larger than 1/4-inch, until beef has just lost its raw pink color, 5 to 7 minutes. Transfer beef mixture to a bowl and stir in cheese until it has melted and blended into mixture. Wipe out skillet with paper towels.

Using 2 tablespoons of oil, thoroughly brush both sides of the tortillas with oil. Arrange tortillas, overlapping, on a rimmed baking sheet into two rows (6 tortillas each). Bake tortillas until warm and pliable, about 5 minutes. Remove tortillas from the oven, and reduce oven temperature to 200°.

Working with one tortilla at a time, place 2 tablespoons of filling on one half of the tortilla. Fold and press to close the tortilla (edges won't seal, but tortilla should remain folded). Continue with remaining filling and tortillas.

Set a wire rack on a rimmed baking sheet and line rack with a double layer of paper towels. Heat remaining 1/4 cup oil in now-empty skillet over medium-high heat until shimmering. Arrange 5-6 tacos in skillet with all tacos facing the same direction (I can only fit 5, but supposedly six can fit with one at the bottom of the pan, then two above, then two more, then one at the top). Cook, adjusting heat so oil actively sizzles and bubbles appear around edges of tacos, until crisp and browned on one side, 2 to 3 minutes. Using tongs and/or a thin spatula, carefully flip tacos. Cook until browned on the second side, 2 to 3 minutes more.

Remove skillet from heat and transfer tacos to prepared rack. Blot tops of tacos with double layer of paper towels. Place the baking sheet in the oven to keep fried tacos warm. Return the skillet to medium-high heat and cook remaining tacos. Serve tacos immediately with garnishes of choice.