In a dry large frying pan over medium-high heat, warm the Mexican simmer sauce base until starting to simmer gently, 2 to 3 minutes. Add the pork or chicken, season lightly with salt and pepper, and cook, stirring occasionally to break into pieces, until combined with the sauce and warmed through, 2 to 4 minutes. Transfer the filling to a large bowl to cool slightly. Wipe out the pan. While the filling is cooking and cooling, prepare the cabbage slaw.

• Cut away any core from the cabbage; thinly slice the cabbage.
• Set aside half the salsa verde for serving.

In a medium bowl, toss together the cabbage, half the salsa verde, and 1 to 2 tablespoons oil; season to taste with salt and pepper. Let stand, stirring occasionally, while you prepare the rest of the meal.

• Remove 6 [12] tortillas from the package; save the rest for another use.
• Crumble the queso fresco if needed. Set aside half for garnish.

On the stovetop directly over a flame, or in the dry pan used for the filling over medium heat, warm the tortillas, turning once, until just pliable and warmed through, about 30 seconds per side.
Place the tortillas on a work surface. Divide the taquito filling evenly among the tortillas, spreading the filling over the bottom third of each tortilla, and sprinkle with half the queso fresco. Roll up each tortilla as tightly as you can.

In the same pan used for the filling, warm 1 to 2 tablespoons oil over medium-high heat until hot but not smoking. Working in batches if needed, place the taquitos, seam side down, and cook, turning once, until the tortillas are crisp and the filling is heated through, 2 to 4 minutes. Transfer to a paper-towel-lined plate. Add more oil between batches if needed.

Transfer the taquitos to individual plates and top with the cabbage slaw, remaining queso fresco, and as much remaining salsa verde as you like.