In large saucepan over high heat, combine potatoes and turnips with enough water to cover.
Bring to a boil and reduce heat to low; cover and simmer 25 to 30 minutes or until vegetables are tender.
Return vegetables to saucepan; heat over high heat for a few seconds to eliminate any excess moisture, shaking saucepan to prevent sticking.
In small saucepan over medium heat, bring milk to a simmer.
In large bowl, mash vegetables.
Stir in warmed milk, Cheddar cheese, butter, TABASCO sauce and salt.