Preheat oven to 475 degrees F. On large jelly-roll pan, toss carrots with oil, cayenne and 1/4 tsp. salt. Spread in single layer and roast, stirring once, until carrots are caramelized - about 30 minutes.
In 5 qt. saucepan, melt butter and add shallots, garlic, thyme, and 1/4 tsp. salt. Cook 3 minutes until shallots are golden, stirring. Add carrots, broth, juice, ginger, and 1/2 tsp salt. Cover. Heat to simmering on med-high. Reduce heat to maintain simmer; cook, partially covered 10 minutes or until tender.
With immersion blender, puree mixture until smooth. Top with yogurt and chives, serve.