Prepare broccoli in microwave according to package directions.
Heat a large ovenproof skillet over medium-high heat. Add oil to pan; swirl to coat. Add onion and mushrooms; cook 12 minutes or until mushrooms brown and liquid evaporates, stirring occasionally. Sprinkle mushroom mixture with flour; cook 1 minute, stirring constantly. Stir in milk. Bring to a boil; cook 3 minutes or until thick and bubbly. Stir in broccoli and chicken; cook 1 minute. Remove pan from heat. Stir in yogurt, mayonnaise, pepper, and salt. Top evenly with cheeses; broil 2 minutes.
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