Heat oven to 375 degrees. Place squash, cut-sides down, on an oiled baking pan. Cook until easily pierced with a knife tip, about 45 minutes. Using a fork, separate the flesh into strands, and transfer to a bowl; cover.
Heat 1 tablespoon oil in a saute pan over medium heat. Cook leeks and shallots, stirring, until crisp, about 10 minutes. Transfer to a plate.
Place flour in a small bowl; dredge scallops. Return pan to heat; add remaining tablespoon oil. Cook half of scallops until golden, about 3 minutes per side. Season with salt and pepper. Cook remaining scallops.
Increase heat to medium high; add wine or 3/4 cup water. Using a wooden spoon, scrape up any brown bits on bottom of pan. Cook until liquid has reduced by half. Slowly whisk in the butter until sauce begins to thicken, about 2 minutes; season with salt and pepper.
Divide the squash and the leek mixture among four dinner plates; top with scallops. Drizzle with sauce, and garnish with chives. Serve.