Butter a 12- by 14-inch piece of foil and set on a baking sheet. In an 8- to 10-inch frying pan over medium-high heat, melt 1/2 cup sugar, frequently shaking and tilting pan. When mixture is a light caramel color (in about 6 minutes), pour onto foil. Let stand until caramel is hard, about 5 minutes. Break into chunks, then, in a food processor or a heavy plastic food bag with a mallet, crush into 1/8- to 1/4-inch pieces.
In a bowl, with an electric mixer on medium speed, beat butter and remaining 1/2 cup sugar until well blended. Beat in 2 tablespoons water and the vanilla until smooth, scraping down sides of bowl as needed.
In another bowl, mix flour and baking powder. Stir or beat into butter mixture until well incorporated. Stir in crushed caramel.
Drop dough in 1 1/2-teaspoon portions, 2 inches apart, onto buttered or cooking parchment-lined 12- by 15-inch baking sheets.
Bake cookies in a 325° oven until edges are light brown, 12 to 15 minutes; if baking more than one pan at a time, switch pan positions halfway through baking.
Let stand on sheets until slightly firm, 1 to 2 minutes, then use a spatula to transfer cookies to racks to cool completely.
Note: Nutritional analysis is per cookie.