Wash, peel, and cube russet potatoes evenly.
Boil potatoes in salted water until fork-tender, about 10 minutes.
Add chopped cabbage and sliced onion to the boiling water; cook for 5 minutes until wilted.
Drain vegetables thoroughly in a colander to remove excess water.
Mash potatoes in a bowl, then fold in shredded cheddar until melted and combined.
Season mashed potatoes with salt and black pepper to taste.
Lay tortillas flat and spread about 1 tablespoon of Thousand Island dressing over half of each tortilla.
Add a generous scoop of cheesy mashed potatoes on the dressed half, then layer with corned beef and cooked cabbage and onions.
Fold tortillas in half and press lightly to compact filling.
Heat a thin layer of oil in a skillet over medium-high heat until shimmering.
Fry tacos in batches until golden and crisp on both sides, about 30 seconds per side.
Drain fried tacos on paper towels to remove excess oil.
Garnish with chopped chives and serve warm with extra Thousand Island dressing.