Stir white sugar, brown sugar, half-and-half, butter, corn syrup, cream of tartar, and salt together in a large, greased saucepan over medium-low heat until caramel mixture boils. Reduce heat to low; cook without stirring until caramel reaches 240 degrees F (115 degrees C) on a candy thermometer, or until a small amount dropped into cold water forms a soft ball, about 25 minutes.
Remove from heat and let cool slightly. Line a baking sheet with greased parchment or greased wax paper.
Insert a caramel apple stick into the middle of each apple. Dip each apple into caramel mixture and turn until fully coated. Place apples on prepared baking sheet until caramel cools completely.