Heat oven to 400°F. Spray 18x13-inch rimmed baking sheet with cooking spray. In 12-inch skillet, melt butter over medium-high heat.
Add cauliflower, onion, garlic, 1/4 teaspoon salt and the pepper.
Cook 4 to 5 minutes, stirring frequently, until cauliflower begins to brown on edges and is tender when pierced with knife.
Stir in broth and milk; heat to boiling over high heat. Reduce heat; simmer 4 to 5 minutes or until cauliflower is very tender.
Remove mixture from heat; cool 5 minutes.
Add cauliflower mixture to blender; cover and blend on high speed 3 to 4 minutes or until completely smooth.
Add cheese; blend 15 to 30 seconds longer or until incorporated. If thinner sauce is desired, add more milk. Wipe out skillet. Return mixture to skillet.
Meanwhile, toss squash noodles with olive oil and 1/2 teaspoon salt; spread evenly on baking sheet.
Roast 9 to 11 minutes or until crisp-tender. Do not overcook. Gently stir into sauce in skillet. Top with parsley.