Preheat oven to 400°.
Cook gnocchi according to package directions, omitting salt and fat. Drain.
Melt butter in a large saucepan over medium heat. Lightly spoon flour into a dry measuring cup; level with a knife. Add flour, salt, and pepper to pan; cook 1 minute, stirring constantly. Gradually add milk and broth, stirring with a whisk until blended. Bring to a boil; cook until thick, stirring constantly. Remove from heat. Add Gruyère, chives, and bacon; stir until smooth. Add gnocchi; toss well.
Spoon mixture into an 11 x 7-inch baking dish coated with cooking spray; sprinkle with Parmesan. Bake at 400° for 20 minutes or until lightly browned. Serve immediately.
Wine note: With creamy dishes like this, the texture of the dish is as important as the flavors. A suitably rich and full-bodied white, like Chardonnay, is a good match for the richness of Gruyère and bacon. Try Mezzacorona Chardonnay Vigneti delle Dolomiti 2005 ($8), from the north of Italy. It offers bright, fresh fruit and a touch of buttery flavor to complement the cheese. -Jeffery Lindenmuth