Preheat a grill to medium. Grill the kielbasa, turning, until marked, 8 to 10 minutes. Transfer to a baking sheet or platter.
Meanwhile, whisk the mustard and vinegar in a large bowl. Slowly whisk in 2 tablespoons olive oil until smooth.
Toss the onion and pierogies with the remaining 2 tablespoons olive oil and season with salt and pepper. Grill, covered, until the pierogies thaw and the onion begins to soften, about 5 minutes. Turn the pierogies and onion and continue to grill, covered, until the pierogies are cooked through and the onion is tender, 4 to 6 more minutes. Transfer to the baking sheet or platter.
Slice the kielbasa into pieces and add to the bowl with the mustard dressing. Roughly chop the onion and add to the bowl along with the pierogies and parsley. Season with salt and pepper and toss. Divide among shallow bowls.