The onions should be cooked until golden—not caramelized—so that they retain some of their allium heat, as well as their sweetness. Slideshow: More Healthy Pasta Recipes
Heat 1 tablespoon of olive oil in a small skillet over moderately high heat. Add the shallot and cook, stirring occasionally, until browned and crisp, about 5 minutes. Remove from the heat and drain on a paper towel-lined plate. Set aside.
Heat the butter and the remaining 2 tablespoons of olive oil in a large skillet over moderate heat. Add the leeks and red and sweet onions, and cook, stirring occasionally, until golden and just tender, 10 to 15 minutes. Season to taste with salt and pepper.
Meanwhile, cook the spaghetti in a large pot of boiling well-salted water until al dente. Set aside 1 cup of the pasta cooking water, then drain well. Add the pasta to the skillet and toss to combine, adding some of the pasta cooking water to moisten the pasta as needed. Top the pasta with the crisp shallots and minced chives and serve immediately.