Melt butter in deep 12-inch skillet over low; stir garlic 30 seconds. Add milk, cooking water, cream, salt, and pepper; gently simmer.
Lay spaghetti in pan; press into liquid as it softens. Partly cover; simmer over medium-low 10 to 13 minutes, stirring and separating every 2 minutes.
Add reserved water in 2-tablespoon amounts only if drying before pasta tender. Uncover final 1 to 2 minutes if excess liquid remains.
Remove from heat; gradually add Parmesan until cooking liquid forms smooth sauce.
Rest 1 minute; stir again and serve while coating loose.