Bring a large pot of salted water to a boil. Add potatoes and cook until tender, about 15 minutes.
Drain potatoes and transfer to a large bowl. Pour in milk and mash until smooth. Stir in onions and cheese; mix well. Spoon 2 heaping tablespoons of potato mixture into the center of each tortilla and fold in half; secure with a toothpick.
In a large skillet add enough oil to reach 1 inch in depth and heat over medium-high heat. Fry tortillas until crispy. Serve with ranch dressing for dipping.
