1. Soak sun-dried tomatoes in boiling water to cover for 20 minutes. Drain, pat dry and chop, or cut with scissors, into small pieces.
2. In a bowl, toss Brie cubes with cornstarch.
3. In a large saucepan or flameproof fondue pot, melt butter over medium heat. Add shallot and cook, stirring until soft, about 3 minutes.
4. Reduce heat to medium-low. Add cheese mixture, a handful at a time, stirring constantly in a figure-eight motion with a wooden spoon until cheese is melted.
5. Stir in sun-dried tomatoes and sugar. Mix well. Remove from heat and set up on a fondue stand with a burner if desired. Serve with bread or other dippers.
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