Position a rack in the middle of the oven and preheat to 400 degrees. In a large bowl, toss the bread cubes with 1/3 cup EVOO and 3/4 tsp. salt; spread in a single layer on a large rimmed baking sheet. Toast in the oven until lightly browned, about 10 minutes. let cool.
Meanwhile, using the same large bowl, combine the carrots, parsnips and onion; toss with the remaining 1/3 cup EVOO and 3/4 tsp. salt. Spread the vegetables in an even layer on 2 large, foil-lined baking sheets. Position racks in the upper and lower thirds of the oven. Roast the vegetables, flipping them and switching the pans halfway through, until tender and slightly browned at the edges, about 25 minutes.
Transfer the vegetables and any pan juices to the large bowl; toss with the toasted bread cubes. Add the lemon juice and parsley, toss again, then season with salt and pepper. Serve warm or at room temperature.