Preheat oven to 400º Fahrenheit. Place 4 medium boneless, skinless chicken breasts top-down in 9x9 baking dish.
Use pastry brush to brush surface of chicken with half of 2 tablespoons butter, covering chicken completely. Sprinkle salt to taste over buttered chicken.
Sprinkle half of 4 tablespoons Everything But the Bagel seasoning over buttered chicken, then carefully flip chicken breasts over.
Brush tops of chicken breasts with remaining butter, sprinkle salt over, and coat with the remaining Everything but the Bagel seasoning.
Place baking dish in preheated oven. Bake chicken 25 to 35 minutes or until internal temperature reaches 160º Fahrenheit.
Once target temperature is reached, carefully remove baking dish from oven. Set aside to rest 5 minutes.
While chicken rests, melt 1 tablespoon butter in medium bowl. Add 1 teaspoon Everything But the Bagel seasoning, 4 ounces cream cheese, 6 tablespoons chopped green onions, and ¼ cup half-and-half to bowl and whisk until fully incorporated into smooth sauce. Taste sauce and add salt as needed
Transfer chicken to serving plates. Spoon plenty of prepared sauce over tops of chicken breasts, then garnish with thinly sliced green onions and Everything But the Bagel seasoning if desired. Serve warm.