Coat a large nonstick skillet with cooking spray; add oil, and place over medium-high heat until hot. Add asparagus and carrot; cook 2 minutes, stirring constantly. Add mushrooms, green onions, and squash; cook 3 minutes or until crisp-tender. Remove from heat; set aside, and keep warm.
Combine flour and next 3 ingredients in a small bowl; gradually add milk, stirring with a whisk until completely blended. Melt butter in a medium saucepan over medium heat. Add garlic, and cook 30 seconds. Add milk mixture to saucepan; cook until thick and bubbly, stirring constantly. Remove saucepan from heat; stir in 1/2 cup Parmesan cheese.
Combine sauce, reserved vegetables, and pasta in a large bowl; toss gently to coat. Sprinkle with remaining 1/4 cup cheese. Sprinkle with additional pepper, if desired.