Preheat the oven to 400 degrees F. Line a baking sheet with foil and spray with nonstick spray.
Slice the spaghetti squash in half lengthwise and scrape out the seeds. Brush the cut sides with olive oil. Place the squash cut-side down on a baking sheet. Roast for 25 minutes.
While the squash is roasting, heat the olive oil in a skillet over medium-low heat. Add the shallots and garlic and cook for 2 minutes. Stir in the broccoli florets and cook, stirring often, for 6 to 8 minutes, until they are slightly softened. Stir in the milk and cook for 1 to 2 minutes, until it is warmed through. Stir in 1 cup of the cheddar and turn off the heat. Stir until the cheddar melts.
Remove squash from the oven and flip them over. Use a fork to scrape some of the squash. Season the squash with salt and pepper. Evenly distribute the broccoli cheddar mix in each squash bowl. Sprinkle the remaining cheddar on top. Sprinkle on the breadcrumbs.
Return the sheet to the oven and bake 10 to 15 minutes, until the cheese is golden and bubbly.