Preheat oven to 375 degrees Fahrenheit.

Arrange leeks, cut side down, in a snug single layer in a shallow 9×13-inch baking dish. Nestle thyme sprigs among the leeks. In a small bowl, mix 1/4 cup olive oil and wine and drizzle over leeks. Sprinkle evenly with salt. Cover tightly with aluminum foil and braise in the oven until completely fork tender, about 45 minutes. Uncover and continue to braise until the leeks are caramelized, another 10 to 15 minutes. Remove thyme and discard.

Toss bread crumbs with remaining tablespoon of olive oil to coat. Spread on a baking sheet in a single layer and bake for five to eight minutes, until crisp.

Transfer leeks to a serving platter and spoon braising liquid over them. Toss bread crumbs with parsley and sprinkle over leeks just before serving. Serve warm or at room temperature.