Preheat the oven to 375 degrees F (190 degrees C). Line a baking sheet with aluminum foil.

Slowly and carefully cut butternut squash in half lengthwise, starting at the stem end. Scoop out seeds with a spoon. Slice off about 1/8 inch from the bottom of each half to ensure they lay flat while baking. Place onto the prepared baking sheet.

Roast in the center of the preheated oven until tender but not falling apart, 60 to 90 minutes. Remove from the oven and let sit until cool enough to handle. Increase the oven temperature to 475 degrees F (245 degrees C).

Use a spoon to scoop squash flesh into a bowl, leaving about 1/2 inch attached to the skin so shells won’t collapse and fall apart later.

Add egg, Dijon, salt, and pepper to squash; mix and mash with a spoon until smooth, or leave it a bit chunky if desired. Stir in green onions, ham, and diced Gruyère; mix until combined.

Scoop mixture back into squash shells, distributing as evenly as possible. Sprinkle grated Gruyère over top.

Bake in the preheated oven until cheese is browned, about 15 minutes.

Remove from the oven and transfer squash halves to a cutting board. Garnish with green onions, cut each half into four slices, and serve.