Heat broiler. In a large pot of water, cook pierogi per package instructions; drain.
Meanwhile, in a large straight-sided skillet over medium-high heat, heat oil. Add peppers, onion, and ¼ teaspoon salt and cook, stirring occasionally, until vegetables are just barely tender, 4 to 6 minutes. Add kielbasa and cook, stirring occasionally, until kielbasa and vegetables are golden in places, 4 to 6 minutes more. Scrape kielbasa mixture onto a plate.
Return skillet to medium heat and add butter and pierogi. Cook, tossing occasionally, until pierogi are golden in places, about 4 minutes. Transfer pierogi to plate with kielbasa mixture.
Increase heat to medium-high. Pour broth into skillet and add cream cheese and mustard. Cook, whisking constantly, until broth comes to a boil and cream cheese is melted. Continue to boil, whisking occasionally, until thickened slightly, about 2 minutes.
Remove skillet from heat. Return pierogi, kielbasa, and vegetable mixture to skillet and stir to coat in sauce. Sprinkle with ¾ cup cheddar and stir a few times to incorporate. Sprinkle top with remaining ½ cup cheddar.
Broil until cheese is melted, 1 to 2 minutes. Top with scallions. Serve with sour cream alongside.
