Grind cinnamon sticks to a fine powder in a coffee grinder; set aside.
Cook sugar and 3 tablespoon butter in a small saucepan over medium-high heat 3 minutes or until melted and golden. Add pecans, and cook 2 minutes until pecans are toasted and glazed, stirring frequently.
Stir in cinnamon and 1/4 teaspoon salt. Spread pecans on wax paper, and set aside to cool.
Combine sweet potatoes, 1/4 cup butter, ginger, 1 teaspoon salt, and nutmeg in a large bowl. Beat at low speed with a hand mixer 1 minute; beat at high speed 2 minutes.
Gently fold crème fraîche, maple syrup, extract, and balsamic vinegar into sweet potatoes. Transfer to a saucepan. Bring to a simmer over medium-low heat. Simmer, covered, 10 minutes, stirring occasionally. Spoon potatoes into a serving dish, and sprinkle with glazed pecans.
*Find crème fraîche with other specialty cheeses in the deli section of many upscale markets.