01 - Preheat oven to 400°F. Slice the spaghetti squash in half lengthwise and scoop out the seeds. Place both halves cut side down on a parchment-lined baking sheet. Roast for 35 to 40 minutes until the flesh is tender and easily shreds into strands with a fork.
02 - While the squash roasts, melt the butter in a medium saucepan over medium heat. Whisk in the flour and cook, stirring constantly, for 1 minute to form a smooth roux.
03 - Gradually pour in the whole milk while whisking continuously. Cook for 2 to 3 minutes, stirring constantly, until the mixture thickens into a smooth béchamel.
04 - Reduce heat to low and add the sharp cheddar, Gruyère, garlic powder, ground mustard, salt, and black pepper. Stir until all the cheeses have fully melted and the sauce is silky and uniform. Remove from heat.
05 - Once the roasted squash is cool enough to handle, use a fork to scrape the flesh into long spaghetti-like strands. Transfer the strands to a large mixing bowl and pour the cheese sauce over top. Gently toss until every strand is evenly coated.
06 - Transfer the sauced squash to a lightly greased baking dish. In a small bowl, combine the breadcrumbs, Parmesan cheese, and melted butter. Sprinkle the mixture evenly over the top. Bake at 400°F for 10 to 12 minutes until the topping is golden and the edges are bubbling.
07 - Remove from the oven and finish with a scattering of freshly chopped chives or parsley. Serve warm.