Heat olive oil in a skillet over medium-high heat. Add diced onion and sauté until soft.
Add ground beef to the skillet, breaking it apart with a spoon. Cook until browned and no longer pink.
Stir in taco seasoning and water. Simmer until the mixture thickens, then remove from heat.
Warm tortillas until pliable, either in the microwave wrapped in a damp towel or in a pan.
Lay a tortilla flat, add a spoonful of beef mixture and sprinkle with cheese. Roll tightly and secure with a toothpick.
For baking: Preheat oven to 425°F. Place taquitos seam-side down on a baking sheet. Bake until crispy, about 15-20 minutes.
For deep-fat frying: Heat oil to 350°F. Fry taquitos until golden brown, then drain on paper towels.
For air-frying: Preheat air fryer to 400°F. Cook taquitos in batches until crispy, about 7 minutes total.
Serve taquitos with your choice of toppings like lettuce, tomatoes, sour cream, salsa, and guacamole.