Preheat oven to 425°. Lightly oil a baking dish or line with parchment paper.

In a large bowl, combine squash, half the minced sage, 2 tablespoons oil, and ½ teaspoon salt; toss well. Transfer squash to prepared baking dish and roast, uncovered, for 35-40 minutes, until fork-tender, stirring every 10 minutes for even browning.

While squash is roasting, in a medium saucepan combine remaining oil, remaining salt, oregano, red pepper flakes, and garlic. Increase heat to medium-high and sauté for 1 minute, stirring frequently. Stir in tomatoes with juices; increase heat to a boil. After 30 seconds reduce heat and simmer for 15 minutes, stirring every few minutes. Add balsamic vinegar, stir for an additional minute, and remove from heat. Taste and add salt, if necessary.

Reduce heat to 400°. Place pitas on baking sheets and bake for 2-3 minutes, until lightly toasted. Remove from oven. Spread each pita with about ¼ cup tomato sauce, leaving a ¼-inch border on the edges. Spread squash over tomato sauce on each pita and top with mozzarella slices. Sprinkle with remaining minced sage. Bake 8-10 minutes, until cheese melts. Cut each pita into fourths, sprinkle with Parmesan cheese and red pepper flakes, and serve hot.