Preheat oven to 375°.
To prepare squash, drizzle 1 tablespoon oil in bottom of a roasting pan. Place squash, cut sides down, and shallots in pan. Bake, uncovered, at 375° for 45 minutes or until tender. Cool. Scoop pulp from squash; discard peels. Reserve 1 1/2 cups pulp. Place remaining 2 tablespoons oil, remaining pulp, shallots, and next 7 ingredients (through garlic) in a food processor; process until smooth.
Reduce oven temperature to 350°.
To prepare pasta, cook pasta in boiling water 7 minutes or until almost tender. Drain. Combine reserved 1 1/2 cups pulp, pureed mixture, pasta, and 1/3 cup cheese in a large bowl; stir gently. Spoon mixture into a 13 x 9-inch baking dish coated with cooking spray; cover with foil.
Bake at 350° for 30 minutes. Uncover; sprinkle with remaining 1/3 cup cheese. Bake 5 minutes or until cheese melts.