1. Place bread cubes in a well-buttered 13- x 9-inch baking dish. Melt 3 Tbsp. butter, and drizzle over bread cubes. Sprinkle with cheeses.
2. Melt remaining 3 Tbsp. butter in a medium saucepan over medium heat; add onion and garlic. Sauté 2 to 3 minutes or until tender. Whisk in flour until smooth; cook, whisking constantly, 2 to 3 minutes or until lightly browned. Whisk in broth and next 4 ingredients until blended. Bring mixture to a boil; reduce heat to medium-low, and simmer, stirring occasionally, 15 minutes or until thickened. Remove from heat. Stir in sour cream. Add salt and pepper to taste.
3. Gradually whisk about one-fourth of hot sour cream mixture into eggs; add egg mixture to remaining sour cream mixture, whisking constantly. Pour mixture over cheese in baking dish. Cover with plastic wrap, and chill 8 to 24 hours.
4. Let strata stand at room temperature 1 hour. Preheat oven to 350°. Remove plastic wrap, and bake 30 minutes or until set. Serve immediately.