Preheat oven to 375°.

Combine squash, broth, milk, and garlic in a medium saucepan; bring to a boil over medium-high heat. Reduce heat to medium, and simmer until squash is tender when pierced with a fork, about 25 minutes. Remove from heat.

Place the hot squash mixture in a blender. Add salt, pepper, and Greek yogurt. Remove the center piece of the blender lid ( to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid ( to avoid splatters). Blend until smooth. Place blended squash mixture in a bowl; stir Gruyere, pecorino Romano, and 2 tablespoons of Parmigiano-Reggiano. Stir until combined.

Cook pasta according package directions, omitting salt and fat; drain well. Add pasta to squash mixture, and stir until combined. Spread mixture evenly into a 13x9-inch glass or ceramic baking dish coated with cooking spray.

Heat oil in a medium skillet over medium heat. Add panko, and cook for 2 minutes or until golden brown. Remove from heat; stir in remaining 2 tablespoons Parmigiano-Reggiano cheese. Lightly coat topping with cooking spray.

Bake at 375° for 25 minutes or until bubbly. Sprinkle with parsley and serve immediately.