Rinse and dry 5 apples (we prefer Granny Smith and Fuji varieties, 6 to 8 oz. each). Insert a craft or popsicle stick halfway into the stem end of each apple. Line a baking sheet with plain parchment paper or wax paper that has been generously coated with butter.
In a bowl set over a pan of simmering water, combine 14 ounces (about 50 pieces) unwrapped soft caramels (such as Kraft) and 2 tablespoons water. Stir frequently until melted and smooth.
Holding the stick, dip each apple one at a time into the caramel about three-quarters of the way. Swirl to coat evenly.
Hold stem side up and use a knife to scrape excess caramel off the bottom of apple back into bowl. Place apples on the parchment paper or buttered waxed paper and refrigerate until caramel is firm, about 5 minutes.
Return pan of water to a boil; remove from heat. Place 10 ounces semisweet or bittersweet chocolate in another bowl and set over pan. Stir frequently until chocolate is melted and smooth.
Dip the bottom half of each apple in chocolate, turning to coat evenly. Hold stem side up and use a knife to scrape excess chocolate off bottom of apple and back into bowl. Place each coated apple on the parchment paper or buttered waxed paper and refrigerate until chocolate is slightly set, about 10 minutes.
Place 1 cup chopped unsalted peanuts on a plate. Roll bottom third of each apple in peanuts to coat. Refrigerate until chocolate is firm, about 15 minutes.