Heat oven to 350°. Coat an 8 x 8-inch baking dish with nonstick cooking spray.
Bring a large pot of salted water to a boil. Add greens to pot and cook for 7 minutes or until tender. Using a slotted spoon, place in a cold water bath, then drain well and squeeze out any excess water; chop finely and set aside.
Heat olive oil in a large skillet over medium heat. Add onion to skillet and cook, stirring occasionally, for 10 minutes or until softened. Stir in garlic and red pepper flakes and cook 1 minute. Stir in mustard greens and bacon; cook 2 minutes or until warmed through. Remove from heat and set aside.
Meanwhile, bring broth, water and salt to a boil over high heat. Reduce heat to low and add polenta in a steady stream. Whisk until well blended. Cook for 2 to 3 minutes or until thickened and smooth. Remove from heat.
Whisk together yogurt and eggs and stir in 1 cup polenta. Add this egg mixture back into the polenta in saucepan. Stir in onion mixture and 1 cup of the mozzarella.
Spread half of polenta mixture into prepared baking dish, then top with 1 cup mozzarella. Spread remaining polenta mixture over top and bake at 350°for 50 minutes or until lightly browned on top. Cool 10 minutes before serving.