Heat the oven to 400 degrees with the rack in the middle position and grease a 9-inch springform pan with vegetable oil spray. Microwave the squash in a covered bowl, stirring occasionally, until completely tender, about 15 to 20 minutes. Process the cooked squash in a food processor until smooth, then set aside to cool.

Heat a portion of the oil in a large nonstick skillet over medium heat until shimmering. Cook the onion until softened, about 5 minutes, then stir in the garlic, coriander, and five-spice until fragrant. Add the squash puree and cook until it thickens slightly, about 2 to 4 minutes; transfer to a large bowl and let cool.

Place the bulgur in a separate bowl and cover with water by 1 inch, letting it sit for 10 minutes until tender. Drain the bulgur through a fine-mesh strainer, then wrap it in a clean dish towel and wring it tightly—you must squeeze out as much moisture as possible to prevent the kibbeh from becoming mushy.

Combine the bulgur, flour, cilantro, mint, salt, and pepper with the squash mixture until the dough is uniform. Press the mixture into an even layer in the prepared pan using wet hands to prevent sticking. Score the surface into eight even wedges with a paring knife, cutting halfway down, then brush with the remaining oil and bake until golden brown and set, about 45 minutes.

Sprinkle the surface with feta and pine nuts and bake for another 10 minutes until the cheese is softened and warmed through. Cool the kibbeh in the pan for 10 minutes to allow it to firm up, then loosen the edges with a thin knife and remove the springform ring. Serve warm, sliced along the scored lines.