Slice in half lengthwise, scoop out seeds, drizzle with a little olive oil and sprinkle with salt and pepper. Place squash flesh side down on a baking sheet. Roast at 350 for 1 hour. Remove from oven and allow to cool. When cool enough to handle, using a fork, scrape flesh of spaghetti squash to release "noodles". Place noodles in bowl and set aside.
Toss broccoli florets with 1 teaspoon olive oil, salt and pepper. Roast in 350 oven for 15 minutes. (I just pop the broccoli in the oven for the last 15 minutes of the spaghetti squash cooking time). Remove from oven and set aside.
Putting it all together:
In a bowl whisk together all dressing ingredients.
Toss spaghetti squash noodles, broccoli, and scallions with dressing. Top with toasted sesame seeds.
To toast sesame seeds - you can buy them toasted but they always taste better to me when I toast them at home. Simply heat a small cast iron skillet over medium heat. Add sesame seeds (make sure the skillet is dry) and toast, stirring often for 3-4 minutes. They will smell nutty and toasty when they are ready.