Microwave the tortillas for 20 seconds to warm them. Place each hot dog in the center of a tortilla, then sprinkle with cheese. Roll the hot dog and cheese in the tortilla, and secure with toothpicks.

In a large, heavy skillet, heat the oil over medium-high heat. When the oil is shimmering, use tongs to carefully place the tortilla-wrapped hot dogs in the oil. Use the tongs to turn the taquitos so that all sides get golden and crisp – you will want to turn about every 20 to 30 seconds. Remove from the skillet and let the excess oil drain off of the taquitos on a paper towel-lined plate. 

When the taquitos are cool enough to handle, remove the toothpicks and carefully cut the taquitos into 1-inch pieces. Serve with Dijon mustard for dipping.