1. Prepare an ice-water bath. Heat sugar and water in a small saucepan over medium-high heat, swirling, until sugar dissolves. Cook, swirling and brushing down sides of pan with a wet pastry brush (to prevent sugar crystals from forming). until dark amber. Immediately dip bottom of pan in ice-water bath to stop the cooking.
2. Place Brie on a serving platter. Dip pecans into caramel using chopsticks; arrange around edge of brie. Rewarm remaining caramel if needed, and pour over top, swirling to coat and drip down sides. Let stand until hardened. Crack caramel with a knife to serve.