Preheat oven to 325°F. Place the chuck roast in a deep roasting pan or Dutch oven. Dissolve the onion soup mix packet in 1 cup of warm water and pour over the meat.
Roast uncovered at 325°F for 34 to 38 minutes per pound — about 3 hours to 3 hours 10 minutes for a 5-lb roast. The meat is ready when it pulls apart easily with two forks.
Remove from oven and let the roast cool slightly. Transfer to the refrigerator and chill overnight. Reserve the pan juices — you'll use them in the filling.
Once fully chilled, shred the roast with two forks or your hands into fine, even strands. Discard any large fat pockets.
Transfer shredded beef to a large mixing bowl. Add the grated cheddar, garlic powder, onion powder, salt and pepper, salsa or diced tomatoes, and finely chopped onion. Mix thoroughly until the filling is consistent and well-seasoned. Add a splash of reserved pan juices if the filling feels too dry.
Warm the tortillas before rolling. Microwave a stack of 8 to 10 wrapped in damp paper towels for 45 to 60 seconds, or dip each tortilla in hot oil for 5 to 8 seconds per side for extra crispiness. Keep them wrapped while you work.
Lay a warm tortilla flat. Spoon about ¼ cup of filling along the lower third. Roll firmly from the bottom, keeping the filling tucked in, and place seam-side down on a baking sheet. Repeat with remaining tortillas and filling.
To fry: Heat oil in a skillet to 300°F. Place taquitos seam-side down first to seal. Fry in batches for 2 to 3 minutes per side until golden and crispy. Drain on paper towels.
To bake: Preheat oven to 400°F. Arrange taquitos seam-side down on a greased baking sheet. Spray tops with cooking spray. Bake 18 to 22 minutes, flipping once halfway through, until golden and firm.
Serve immediately with sour cream, salsa, guacamole, or cheese sauce on the side.