Combine first 3 ingredients in a large bowl; cover and chill 30 minutes.
Preheat oven to 350°.
Heat olive oil in a medium skillet over medium-high heat. Add onion; sauté 3 minutes. Add onion, feta and Parmesan cheeses, chopped mint, and black pepper to squash mixture, stirring to combine.
Working with 1 phyllo sheet at a time (cover remaining dough to prevent drying), place 1 sheet into a 10-inch deep-dish pie plate coated with cooking spray. Gently press sheet into pie plate, allowing ends to extend over edges of pan; lightly coat with cooking spray. Place another phyllo sheet across first sheet to form a crisscross design; lightly coat phyllo with cooking spray. Repeat procedure with 2 phyllo sheets and cooking spray.
Spoon squash mixture over phyllo. Place another phyllo sheet over squash, repeating crisscross design with remaining phyllo and cooking spray. Fold in edges of phyllo to fit dish and form a rim. Bake at 350° for 40 minutes or until golden brown.
This is a great vegetarian main dish, that receives rave reviews every time I have served it. While I generally follow the recipe instructions, I have found that increasing the bulgur to 1/2 cup improves the filling. Extra phyllo dough sheets can be used for a crispier pie. I have subbed in spinach (frozen and drained) instead of the butternut squash with good outcomes. This dish is on bi-weekly rotation when butternut squash is in season.
I was slightly skeptical of this dish before making but it turned out wonderful! The mint made it so fresh. I had never worked with phyllo before and it was easier than I imagined. Very yummy. I will make this again.
I was really surprised that this dish did not do much for me, I love all the ingredients. But the outcome was just kind of ok. I will say that the presentation is really nice, and it is an interesting dish. I doubt I'd make it again, or be tempted to take seconds.