Prep ingredients: Preheat oven to 425°F with a rack in the upper third. Finely chop onion. Halve poblano pepper, discard stem and seeds, then finely chop. Finely chop all of the cheddar. Finely chop 2 teaspoons garlic. Generously oil a rimmed baking sheet. Using your fingers, break pulled pork up into bite-size pieces.

Cook filling: Heat 1 tablespoon oil in a medium skillet over medium-high. Add peppers and all but 2 tablespoons of the onions; cook, stirring, until softened and golden brown, about 5 minutes. Add pulled pork and half of the chopped garlic; cook, breaking up pork with a spoon. Stir in ½ cup water; simmer, scraping up browned bits, 1 minute. Season to taste with salt and pepper.

Assemble flautas: Place tortillas on a work surface; spoon about ⅓ cup of the pork filling onto one half of each tortilla, and spread to a 4- x1-inch rectangle. Top with some of the cheese, then roll tightly, starting at the filled side of the tortilla. Place flautas on prepared baking sheet, seam side down. Wipe out skillet and reserve for step 5.

Bake flautas: Generously brush tops and sides of flautas with oil. Bake on upper oven rack until golden brown and crispy, 15–20 minutes (watch closely as ovens vary).

Make taco sauce: Heat 1 tablespoon oil in reserved skillet over medium-high. Add 2¼ teaspoons taco seasoning and remaining chopped garlic; cook, stirring, until garlic is sizzling, about 1 minute. Stir in tomato sauce and ½ cup water, and bring to a boil. Simmer over medium heat until sauce is slightly thickened, about 5 minutes. Season to taste with salt and pepper.

Finish & serve: Coarsely chop cilantro leaves and stems together. In a small bowl, thin all of the sour cream by adding 1 teaspoon water as needed. Season to taste with salt and pepper. Serve flautas topped with some of the taco sauce, sour cream, remaining chopped onions, and cilantro. Serve remaining taco sauce on the side, for dipping.