Step 1

Bring pork shoulder roast, onion, garlic, and 1 package taco seasoning to a boil in a large pot with enough water to cover. Reduce heat to medium-low and simmer until tender and no longer pink in the center, 2 to 3 hours. Check water level every 45 minutes, adding more as needed. Reserve about 1 cup cooking liquid.

Step 2

Shred pork with a fork, discarding excess fat and bone. Stir in tomatoes, refried beans, green chiles, and remaining package of taco seasoning. If the mixture is too dry, add reserved cooking liquid.

Step 3

Spread pork mixture evenly down the center of each tortilla; sprinkle with Cheddar cheese. Fold bottom and top edges of each tortilla over filling; roll sides up to enclose filling completely.

Step 4

Heat 2 tablespoons vegetable oil a large skillet over medium heat; fry burritos in batches, seam sides down, until tortillas are golden, about 2 minutes per side. Drain fried burritos on a paper towel-lined plate.