Preheat the oven to 400 degrees F. Line a baking sheet with foil.
Place the chopped greens on the foil. Drizzle with olive oil and gently toss. Top the greens with another piece of foil and seal shut. Roast the greens until tender, about 20 minutes.
Place the bread cubes, sun-dried tomatoes, vinegar, extra-virgin olive oil, salt, and pepper in a large bowl. Gently toss. Add the roasted chard and toss to combine. Serve.