Trim off the roots and dark green parts of the leeks. Slice the leeks in half lengthwise. Place the leeks in a large bowl of cold water, cut side down, and allow them to sit about 10 minutes, until the grit falls to the bottom of the bowl. Lift the leeks out of the bowl and change the water, rinsing the leeks again, checking between the folds to make sure all the grit is gone. Dry the leeks with a paper towel.
Spray a 9x13" baking dish with nonstick cooking spray. Set the leeks in the baking dish, cut side up. Brush with the olive oil. Roast 20 minutes, tossing halfway through to make sure they don't get too brown. Pour vegetable broth over the leeks. Roast another 10 minutes or until leeks are tender. Season with kosher salt and pepper. Serve immediately.